1. Use the interference intensity formula

For two coherent beams of intensities $I_1$ and $I_2$, the resultant intensity is

$I = I_1 + I_2 + 2\sqrt{I_1 I_2}\cos\phi$

where $\phi$ is the phase difference.

Here,

$I_1 = 4I, \qquad I_2 = 9I$

2. Intensity at point A

At point A, phase difference is zero:

$\phi_A = 0 \Rightarrow \cos 0 = 1$

So,

$I_A = 4I + 9I + 2\sqrt{(4I)(9I)}$

$I_A = 13I + 2\sqrt{36I^2}$

$I_A = 13I + 12I = 25I$

3. Intensity at point B

At point B, phase difference is $\pi$:

$\phi_B = \pi \Rightarrow \cos \pi = -1$

So,

$I_B = 4I + 9I + 2\sqrt{(4I)(9I)}(-1)$

$I_B = 13I - 12I = I$

4. Difference of resultant intensities

$I_A - I_B = 25I - I = 24I$

So the required difference is

$\boxed{24}$

5. Comparison with stored answer

Stored correct answer = $24$

Our derived answer = $24$

They match.