The distance between the line and the point is:
$$ d = \frac{ 23 \sqrt{ 10}}{ 10 } $$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
$$\begin{aligned} y & = 3 x - 1 \\3x-y-1&=0\end{aligned}$$After substituting: $ A = 3 $ , $ B = -1 $ , $ C = -1 $ , $ x_0 = -6 $ and $ y_0 = 4 $ we have:
$$ \begin{aligned} d =& \frac{ \left| 3\cdot\left(-6\right) +\left(-1\right)\cdot4 + \left( -1\right) \right| }{\sqrt{ 3^2 + (-1)^2}} = \\ d =& \frac{ \left| -18 -4 -1 \right| }{\sqrt{ 9 + 1}} = \\ d =& \frac{ \left| -23 \right| }{\sqrt{ 10}} = \\ d =& \frac{ 23 }{ \sqrt{ 10 } } = \\ d =& \frac{ 23 \sqrt{ 10}}{ 10 } \end{aligned} $$