Solve the equation 43x+2 = 26x+2x for x. Options are A) x=1, B) x=0, C) x=-1, D) x=2, E) x=3

The given equation is $4^{3x+2} = 2^{6x+2x}$.
First, simplify the exponent on the right side:

$$4^{3x+2} = 2^{8x}$$

Since $4 = 2^2$, substitute this into the equation:

$$(2^2)^{3x+2} = 2^{8x}$$

Multiply the exponents on the left side:

$$2^{2(3x+2)} = 2^{8x}$$ $$2^{6x+4} = 2^{8x}$$

Since the bases are the same, the exponents must be equal:

$$6x+4 = 8x$$

Subtract $6x$ from both sides of the equation:

$$4 = 8x - 6x$$ $$4 = 2x$$

Divide by 2:

$$x = \frac{4}{2}$$ $$x = 2$$

Comparing this result with the given options, $x=2$ corresponds to option D.

The final answer is $\boxed{\text{D}}$.