To solve the equation \(-4(6x - 8) = -24x + 32\), we will first distribute \(-4\) on the left side:
\[ -4 \cdot 6x + (-4) \cdot (-8) = -24x + 32 \]
This simplifies to:
\[ -24x + 32 = -24x + 32 \]
Now, we can observe that the left side and the right side of the equation are identical:
\[ -24x + 32 = -24x + 32 \]
Since both sides of the equation are equal for any value of \(x\), this means that the equation has infinitely many solutions.
Thus, the answer is:
B: Infinitely many solutions.