We are given the graph of a function $h(x)$ and we are asked to find the value of $h(-4)$ and $h^{-1}(-3)$.

1. Problem Description

We are given the graph of a function $h(x)$ and we are asked to find the value of $h(-4)$ and $h^{-1}(-3)$.

2. Solution Steps

A. To find $h(-4)$, we look at the graph of $h(x)$ and find the $y$-value when $x=-4$. From the graph, we see that when $x=-4$, $y=6$. Therefore, $h(-4)=6$.

B. To find $h^{-1}(-3)$, we need to find the value of $x$ such that $h(x)=-3$. In other words, we look for the $x$-value when the $y$-value is $-3$. From the graph, we see that when $y=-3$, $x=2$. Therefore, $h^{-1}(-3)=2$.

3. Final Answer

$h(-4) = 6$

$h^{-1}(-3) = 2$