Answer
$\mathbf v=\langle 2,2\sqrt 3\rangle$
Work Step by Step
The component form of a vector $\mathbf v$ that make an angle $\theta$ with the positive $x$-axis is given by:
$$\mathbf v=\langle |\mathbf v|\cos(\theta),|\mathbf v|\sin(\theta)\rangle$$
Substitution:
$$\mathbf v=\langle 4\cos(\frac{\pi}{3}),4\sin(\frac{\pi}{3})\rangle$$
$$\mathbf v=\langle 4\cdot \frac{1}{2},4\cdot \frac{\sqrt 3}{2}\rangle$$
$$\mathbf v=\langle 2,2\sqrt 3\rangle$$