To find the value of \( h(3) \), we start with the given function \( h(x) = f(x) + 4 \).
From the table, we see that \( f(3) = -10 \).
Now, we calculate \( h(3) \):
\[ h(3) = f(3) + 4 = -10 + 4 = -6 \]
Thus, the value of \( h(3) \) is \(-6\).
The correct choice is:
\[ -6 \]