Answer
$$\operatorname{proj}_{{v}} {u}
=\frac{12}{16}(0,4).$$
Work Step by Step
Let $u=(2,3)$, $v=(0,4)$, $\langle{u}, {v}\rangle=u\cdot v$. Then, we have
$$\langle{u}, {v}\rangle=12, \quad \langle{v}, {v}\rangle=16.$$
Now, the orthogonal projection of $u$ onto $v$ is given by
$$\operatorname{proj}_{{v}} {u}
=\frac{\langle{u}, {v}\rangle}{\langle{v}, {v}\rangle} {v}=\frac{12}{16}(0,4).$$
