Let's look at Quantity A:
2^8 * 3^15 + 2^8 * 3^15

Factor out 2^8
2^8 (1 * 3^15 + 1 * 3^15) which is just 2^8(3^15 + 3^15)

Again we can factor out 3^15
2^8 * 3^15(1 + 1)

2^8 * 3^15(2)

Using the exponent rule x^a * x^b = x^a+b, we have
2^8 +1 -------- because the 2 in the bracket is raised to the power of 1

Final answer for A
2^9 *3^15


Quantity B
6^9 * 3^6
-- 6 can be broken into 2*3

(2*3)^9 * 3^6

Distribute the power of 9
2^9 * 3^9 * 3^6

2^9 * 3^9+6

Final answer for B
2^9 * 3^15

Therefore A and B are equal