Let's solve each of the given expressions step-by-step.

### Expression 1: \(-\frac{3}{4} \cdot \frac{12}{-5} \cdot \left( -\frac{25}{6} \right)\)

1. Multiply the fractions:
\[
-\frac{3}{4} \cdot \frac{12}{-5} = \frac{3 \cdot 12}{4 \cdot 5} = \frac{36}{20} = \frac{9}{5}
\]
Note that the negative signs cancel out.

2. Now multiply the result by \(-\frac{25}{6}\):
\[
\frac{9}{5} \cdot \left( -\frac{25}{6} \right) = -\frac{9 \cdot 25}{5 \cdot 6} = -\frac{225}{30} = -\frac{15}{2}
\]

So, the result of Expression 1 is \(-\frac{15}{2}\).

### Expression 2: \(-2 \cdot \frac{-38}{21} \cdot \frac{-7}{4} \cdot \left( -\frac{3}{8} \right)\)

1. Multiply \(-2\) by \(\frac{-38}{21}\):
\[
-2 \cdot \frac{-38}{21} = \frac{76}{21}
\]

2. Multiply the result by \(\frac{-7}{4}\):
\[
\frac{76}{21} \cdot \frac{-7}{4} = \frac{76 \cdot -7}{21 \cdot 4} = \frac{-532}{84} = -\frac{266}{42} = -\frac{133}{21}
\]

3. Multiply the result by \(-\frac{3}{8}\):
\[
-\frac{133}{21} \cdot \left( -\frac{3}{8} \right) = \frac{133 \cdot 3}{21 \cdot 8} = \frac{399}{168} = \frac{133}{56}
\]

So, the result of Expression 2 is \(\frac{133}{56}\).

### Expression 3: \(\frac{11}{12} \div \frac{33}{16} \cdot \frac{3}{5}\)

1. Divide \(\frac{11}{12}\) by \(\frac{33}{16}\):
\[
\frac{11}{12} \div \frac{33}{16} = \frac{11}{12} \cdot \frac{16}{33} = \frac{11 \cdot 16}{12 \cdot 33} = \frac{176}{396} = \frac{88}{198} = \frac{44}{99} = \frac{4}{9}
\]

2. Multiply the result by \(\frac{3}{5}\):
\[
\frac{4}{9} \cdot \frac{3}{5} = \frac{4 \cdot 3}{9 \cdot 5} = \frac{12}{45} = \frac{4}{15}
\]

So, the result of Expression 3 is \(\frac{4}{15}\).

### Expression 4: \(\frac{7}{23} \cdot \left[ -\frac{8}{6} - \frac{45}{18} \right]\)

1. Simplify inside the brackets:
\[
-\frac{8}{6} = -\frac{4}{3}
\]
\[
\frac{45}{18} = \frac{5}{2}
\]

2. Combine the fractions inside the brackets:
\[
-\frac{4}{3} - \frac{5}{2} = -\frac{8}{6} - \frac{15}{6} = -\frac{23}{6}
\]

3. Multiply the result by \(\frac{7}{23}\):
\[
\frac{7}{23} \cdot \left( -\frac{23}{6} \right) = -\frac{7 \cdot 23}{23 \cdot 6} = -\frac{7}{6}
\]

So, the result of Expression 4 is \(-\frac{7}{6}\).

### Summary of Results:
1. \(-\frac{15}{2}\)
2. \(\frac{133}{56}\)
3. \(\frac{4}{15}\)
4. \(-\frac{7}{6}\)