Great question!
I love that we can eliminate 4 answer choices by inspection.

For example, if x = 3 (answer choice E), then we can see that we get: (3 – 3)(3 + 2) = (3 – 2)(3 + 3)
Simplify (in head) to get: (ZERO)(non-zero #) = (non-zero #)(non-zero #)
This equation cannot hold true. So ELIMINATE E

Using the same logic we can also ELIMINATE A, B and D, which leaves us with C, the correct answer.

-----------------------------------------------------

The LONGER approach is to EXPAND and SOLVE

Given: (x – 3)(x + 2) = (x – 2)(x + 3)
Expand and simplify: x² - x - 6 = x² + x - 6
Add 6 to both sides to get: x² - x = x² + x
Subtract x² from both sides to get: -x = x
Add x to both sides: 0 = 2x
Solve: x = 0

Answer: C