Answer
The answer is
$$h=3.0\text{ m}.$$
Work Step by Step
If the dolphin is moving horizontally through the hoop, that means that its vertical component of the velocity is equal to zero, and this happens only at the highest point of the trajectory. The dolphin has to stop ascending at that point so the required height is equal to the stopping length for its initial value of vertical component of the velocity i.e.
$$h=\frac{v_{y0}^2}{2g}=\frac{v_0^2\sin^240.0^\circ}{2g}=\frac{12.0^2\cdot\sin^240.0^\circ}{2\cdot 9.81}\text{ m}=3.0\text{ m}.$$
