We are given that $x=2$ is a root of the equation $4x^3 + kx - 24 = 0$. We need to find the value of $k$.

1. Problem Description

We are given that $x=2$ is a root of the equation $4x^3 + kx - 24 = 0$. We need to find the value of $k$.

2. Solution Steps

Since $x=2$ is a root of the equation $4x^3 + kx - 24 = 0$, we can substitute $x=2$ into the equation and solve for $k$.

Substituting $x=2$ into the equation gives us:

$4(2)^3 + k(2) - 24 = 0$

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

$32 + 2k - 24 = 0$

$8 + 2k = 0$

$2k = -8$

$k = \frac{-8}{2}$

$k = -4$

3. Final Answer

The value of $k$ is $-4$.