Obviously, A isn't 0 or 1. Because the product (JIG) has only three digits, A x D can't be greater than 9. There are four possible combinations of A and D:

A = 2, D = 3
A = 2, D = 4
A = 3, D = 2
A = 4, D = 2

A x I must be a two-digit number ending in I. A cannot be an even number; no even number would cause this result with I. A must be 3. I must be 5. Therefore, the answer is 252 x 3 = 756.