Answer
False
Work Step by Step
We are given the functions:
$f(x)=\sqrt x$
$h(x)=-\sqrt{x+9}-13$
We start with the function $f(x)=\sqrt x$. Horizontally shift it 9 units to the left to get $\sqrt{x+9}$, then reflect it across the $x$ axis to get $-\sqrt{x+9}$. Then vertically shift it 13 units downward to get $h(x)$.
The given statement is false because the order of the last two transformations have to be reversed.