A vector in x - y plane makes an angle of 30 ^ o with y -axis. The...

The angle made by the vector on $xaxis$ is

$\theta = 90 ° - 30 ° = 60 °$

Let the vector be $\overset{\to}{a}$.

It is given that

${a}_{y} = 2\sqrt{3} ⇒ asin60 ° = 2\sqrt{3} ⇒ \dfrac{a\sqrt{3}}{2} = 2\sqrt{3} ⇒ a = 4$

$x$ component is ${a}_{x} = acos60 ° ⇒ {a}_{x} = 4 \times \dfrac{1}{2} = 2$