To solve this equation, we can use the properties of logarithms.

First, we can combine the logarithms on the left side of the equation using the properties of logarithms:
log4(x^2) + logx^6 64 = 2
log4(x^2 * x^6) = 2
log4(x^8) = 2

Next, we can rewrite the equation in exponential form:
4^2 = x^8
16 = x^8

Taking the 8th root of both sides gives us the final solution:
x = ±2

Therefore, the solution to the equation log4(x^2) + logx^6 64 = 2 is x = ±2.