Step 1 :The function $h(x)$ is defined as the sum of the functions $f(x)$ and $g(x)$.
Step 2 :We know that $f(-2) = 3$ and $g(-2) = 4$.
Step 3 :Therefore, $h(-2) = f(-2) + g(-2) = 3 + 4 = 7.
Step 4 :So, the ordered pair for $h(x)$ is $(-2, 7)$.
Step 5 :Therefore, $a = 2$ and $b = 7$.
Step 6 :Final Answer: The values of $a$ and $b$ are $a = \boxed{2}$ and $b = \boxed{7}$.