To solve the problem, we need to analyze the triangle \( \Delta ABC \) given the information:

1. **For part a**: Given \( AB = 5 \) cm, \( AC = 12 \) cm, and that \( \angle A = 90^\circ \):
- We can find \( BC \) using the Pythagorean theorem:
\[
BC^2 = AB^2 + AC^2
\]
\[
BC^2 = 5^2 + 12^2 = 25 + 144 = 169
\]
\[
BC = \sqrt{169} = 13 \, \text{cm}
\]

2. **For part b**: Here, it states \( AB = 8\sqrt{3} \) and \( BC = 6 \):
- Again, use the Pythagorean theorem:
\[
AC^2 = BC^2 - AB^2
\]
\[
AC^2 = 6^2 - (8\sqrt{3})^2 = 36 - 192 = -156
\]
This would indicate a contradiction since side lengths in a triangle cannot yield a negative square.

Thus, the first part is valid, while the second part is not possible with the stated lengths.