Để giải tam giác ABC với các thông tin đã cho: \( AB = 4 \) cm, góc \( B = 60^\circ \), và góc \( C = 45^\circ \), ta có thể làm theo các bước sau:

1. **Tính góc A:**
Tổng các góc trong một tam giác bằng \( 180^\circ \). Do đó, ta có:
\[
A = 180^\circ - B - C = 180^\circ - 60^\circ - 45^\circ = 75^\circ
\]

2. **Sử dụng định lý sin để tính các cạnh còn lại:**
Định lý sin cho tam giác ABC là:
\[
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
\]
Trong đó:
- \( a \) là độ dài cạnh BC
- \( b \) là độ dài cạnh AC
- \( c \) là độ dài cạnh AB (đã biết \( c = 4 \) cm)

Ta có:
\[
\frac{a}{\sin 75^\circ} = \frac{b}{\sin 45^\circ} = \frac{4}{\sin 60^\circ}
\]

3. **Tính giá trị của sin các góc:**
- \( \sin 75^\circ = \sin(45^\circ + 30^\circ) = \sin 45^\circ \cos 30^\circ + \cos 45^\circ \sin 30^\circ = \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{3}}{2} + \frac{\sqrt{2}}{2} \cdot \frac{1}{2} = \frac{\sqrt{6} + \sqrt{2}}{4} \)
- \( \sin 60^\circ = \frac{\sqrt{3}}{2} \)
- \( \sin 45^\circ = \frac{\sqrt{2}}{2} \)

4. **Tính cạnh a (BC):**
\[
\frac{a}{\sin 75^\circ} = \frac{4}{\sin 60^\circ} \Rightarrow a = \frac{4 \sin 75^\circ}{\sin 60^\circ}
\]
\[
a = \frac{4 \cdot \frac{\sqrt{6} + \sqrt{2}}{4}}{\frac{\sqrt{3}}{2}} = \frac{(\sqrt{6} + \sqrt{2})}{\frac{\sqrt{3}}{2}} = \frac{2(\sqrt{6} + \sqrt{2})}{\sqrt{3}} = \frac{2\sqrt{6} + 2\sqrt{2}}{\sqrt{3}} = \frac{2\sqrt{6}}{\sqrt{3}} + \frac{2\sqrt{2}}{\sqrt{3}} = 2\sqrt{2} + \frac{2\sqrt{2}}{\sqrt{3}}
\]
\[
a = 2\sqrt{2} + \frac{2\sqrt{2}}{\sqrt{3}} = 2\sqrt{2}(1 + \frac{1}{\sqrt{3}}) = 2\sqrt{2}(1 + \frac{\sqrt{3}}{3}) = 2\sqrt{2} \cdot \frac{3 + \sqrt{3}}{3} = \frac{2\sqrt{2}(3 + \sqrt{3})}{3}
\]

5. **Tính cạnh b (AC):**
\[
\frac{b}{\sin 45^\circ} = \frac{4}{\sin 60^\circ} \Rightarrow b = \frac{4 \sin 45^\circ}{\sin 60^\circ}
\]
\[
b = \frac{4 \cdot \frac{\sqrt{2}}{2}}{\frac{\sqrt{3}}{2}} = \frac{4 \cdot \frac{\sqrt{2}}{2}}{\frac{\sqrt{3}}{2}} = \frac{2\sqrt{2}}{\frac{\sqrt{3}}{2}} = \frac{2\sqrt{2} \cdot 2}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}} = \frac{4\sqrt{2}}{\sqrt{3}}