Find the coordinates of v → if v → = 2 a → − 3...

Step 1
From what I understand, $\overrightarrow{u}(p;q)$ means that $\overrightarrow{u}$ is a vector in ${\mathbb{R}}^2$ , with coordinates (p, q). So,
$\overrightarrow{v}=2\overrightarrow{a}-3\overrightarrow{b}+4\overrightarrow{c}=2(4,1)-3(1,2)+4(2,7)=(13,24)$
In your notation, $\overrightarrow{v}(13;24)$

Step 1
I am supposing that by "find the coordinates" it means cartesian coordinates, and that $\overrightarrow{a}(4;1)$ is the same as writing:
$\overrightarrow{a}=\left(\begin{array}{c}4\\ 1\end{array}\right)$
where 4 is the x component, and 1 is the y component. Then you have a vector determined by three others, but, because you are in the plane ${\mathbb{R}}^2$, it is redundant. So you are looking to reduce the number of "coordinates" (numbers by which you label your vector) to two, which is the minimum. As delta-divine has said, the result would be
$\overrightarrow{v}=\left(\begin{array}{c}13\\ 24\end{array}\right)$
which is $\overrightarrow{v}(13;24)$ in your notation.