To solve the equation 8^2.2^n = 4^15, we can rewrite both sides of the equation using the same base.

8^2.2^n = (2^3)^2.2^n = 2^(3*2).2^n = 2^(6+2n)

4^15 = (2^2)^15 = 2^(2*15) = 2^30

Now we have the equation 2^(6+2n) = 2^30.

Since the bases are the same, we can equate the exponents:

6 + 2n = 30

Subtracting 6 from both sides:

2n = 24

Dividing both sides by 2:

n = 12

Therefore, the value of n that satisfies the equation is 12.