The equation will have infinitely many solutions when \( h = -12 \) because you get infinitely many solutions when you have the same coefficient of \( x \) on either side of the equation, and the constant terms are also equal.
To set it up, we want the expressions on both sides to be equivalent:
\[ h(-3x + 6) = -12x + 24 \]
For this to have infinitely many solutions, the coefficients of \( x \) must match:
\[ h(-3) = -12 \implies h = 4 \]
And the constant terms must also be equal when substituting \( h = 4 \):
\[ h \cdot 6 = 24 \implies 4 \cdot 6 = 24 \]
Thus, \( h = 4 \) ensures there are infinitely many solutions.