Choice A is the correct answer. Rewrite with base 2 and solve.

1. Rewrite: $4 = 2^2$ and $8 = 2^3$.
2. Substitute: $(2^2)^x = (2^3)^{x-2}$.
3. Simplify: $2^{2x} = 2^{3(x-2)} = 2^{3x-6}$.
4. Equal bases: $2x = 3x - 6$.
5. Solve: $-x = -6$, so $x = 6$.
6. Verify: $4^6 = 4096$ and $8^4 = 4096$ ✓

💡 Strategic Tip: Convert to a common base (usually smallest prime).

Choice B is incorrect because$4^4 = 256$ and $8^2 = 64$, not equal. Choice C is incorrect because this gives different values. Choice D is incorrect because$4^2 = 16$ and $8^0 = 1$, not equal.