The distance between the line and the point is:
$$ d = \frac{ 22 \sqrt{ 17}}{ 17 } $$The distance from the point $ (x_0, y_0) $ to the line $ Ax + By + C = 0 $ is given by:
$$ d = \frac{ \left| Ax_0 + B_yo + C \right| }{ \sqrt{A^2 + B^2}} $$To apply this formula, we first need to express the line in standard form
$$\begin{aligned} y & = - 4 x \\4x+y&=0\end{aligned}$$After substituting: $ A = 4 $ , $ B = 1 $ , $ C = 0 $ , $ x_0 = 6 $ and $ y_0 = -2 $ we have:
$$ \begin{aligned} d =& \frac{ \left| 4\cdot6 +1\cdot\left(-2\right) + 0 \right| }{\sqrt{ 4^2 + 1^2}} = \\ d =& \frac{ \left| 24 -2 + 0 \right| }{\sqrt{ 16 + 1}} = \\ d =& \frac{ \left| 22 \right| }{\sqrt{ 17}} = \\ d =& \frac{ 22 }{ \sqrt{ 17 } } = \\ d =& \frac{ 22 \sqrt{ 17}}{ 17 } \end{aligned} $$