Explanation:

Let’s break down the question:

- The number of terms in the expansion of (3x - y )4 is 5 (since terms = power + 1 for two variables).

- The number of terms in (x + 3y )4 is also 5.

- When multiplying two expansions, the number of distinct terms in the final result is the number of different powers that can be obtained by multiplying terms.

- Generally, when two expressions (each of degree n) in two variables are multiplied, the maximum possible terms = 2n + 1.

- For n = 4, the number of distinct terms is 9.

- But, let's see why: Final terms will be of the form x^r y^(8-r) for r = 0 to 8, so 9 terms.

Let’s analyze the options:

- Option 1: 9 Correct—because terms will be x8, x7y, ... y8 for r from 0 to 8

- Option 2: 12 ? Not correct, as explained above.

- Option 3: 15 ? Too high for this combination.

- Option 4: 17 ? Way too high, doesn't match the expansion logic.

Correct Option:

Option 1: 9