Choice A is the correct answer. The area of a rectangle is $\text{Area} = \text{Length} \times \text{Width}$.

1. We are given Area $= x^2 + 5x + 6$ and Width $= (x + 2)$.
2. We need to find the other factor of the quadratic.
3. Factor $x^2 + 5x + 6$: We need numbers that multiply to 6 and add to 5. They are 2 and 3.
4. So, $x^2 + 5x + 6 = (x + 2)(x + 3)$.

Since the width is $(x + 2)$, the length must be $(x + 3)$.

Choice B is incorrect because $(x+2)(x+4) = x^2 + 6x + 8$. Choice C is incorrect because $(x+2)(x+2) = x^2 + 4x + 4$. Choice D is incorrect because $(x+2)(x+1) = x^2 + 3x + 2$.