If (x+2) and (x-1) are factors of 2kx2 + Lx + 24, find the values of L and k.

If $(x+2)$ is a factor, then $P(-2) = 0$.
Substitute $x = -2$ into the polynomial:

$$P(-2) = 2k(-2)^2 + L(-2) + 24 = 0$$ $$2k(4) - 2L + 24 = 0$$ $$8k - 2L + 24 = 0$$

Divide the entire equation by 2:

$$4k - L + 12 = 0$$

Rearrange to express $L$ in terms of $k$:

$$L = 4k + 12 \quad (*)$$

If $(x-1)$ is a factor, then $P(1) = 0$.
Substitute $x = 1$ into the polynomial:

$$P(1) = 2k(1)^2 + L(1) + 24 = 0$$ $$2k + L + 24 = 0 \quad (**)$$

Substitute equation $(*)$ into equation $(**)$:

$$2k + (4k + 12) + 24 = 0$$ $$6k + 36 = 0$$ $$6k = -36$$ $$k = \frac{-36}{6}$$ $$k = -6$$

$$L = 4k + 12$$ $$L = 4(-6) + 12$$ $$L = -24 + 12$$ $$L = -12$$

Thus, the values are $L = -12$ and $k = -6$.

Comparing this with the given options:
A. L = -12, k = -6
B. L = -2, k = 1
C. L = -2, k = -1
D. L = 0, k = 1

The calculated values match option A.

The final answer is $\boxed{\text{A. L = -12, k = -6}}$.