Answer
$h=1.49m$
Work Step by Step
The skateboarder reaches his highest point when his speed equals $0$. Reaching the highest point from his initial position means there is a decrease in KE: $$\Delta KE=\frac{1}{2}m(v_f^2-v_0^2)$$
As shown, his final speed $v_f=0$ and $v_0=5.4m/s$. So, $$\Delta KE=\frac{1}{2}m(-29.16)=-14.58m$$
This decrease in KE means an increase in PE. In detail, $$\Delta PE=-\Delta KE=14.58m$$ $$mgh=14.58m$$ ($h$ is the difference in height as shown in the drawing) $$gh=14.58$$ $$h=\frac{14.58}{9.8}=1.49m$$
