The equation of the line passing through point $ \left(-12,~14\right) $, and point $ \left(6,~-1\right) $ is:
$$ 5x+6y-24=0 $$To find equation of the line passing through points $ A(x_A,y_A) $ and $ B(x_B,y_B) $, we use formula:
$$ y - y_A~=~\frac{y_B - y_A}{x_B - x_A}(x-x_A) $$In this example we have:
$$ \begin{aligned} & \left(-12,~14\right) \implies x_A = -12 ~~\text{and}~~ y_A = 14 \\[1 em] & \left(6,~-1\right) \implies x_B = 6 ~~\text{and}~~ y_B = -1 \end{aligned} $$After substituting into the formula, we obtain:
$$ \begin{aligned} y - y_A~&=~\frac{y_B - y_A}{x_B - x_A}(x - x_A) \\[1 em] y - 14~&=~\frac{ -1 - 14 }{ 6 - \left(-12\right) } \left( x - \left(-12\right) \right) \\[1 em]y - 14 ~&=~ -\frac{ 5 }{ 6 } \left( x + 12 \right) \\[1 em]y - 14 ~&=~ -\frac{ 5 }{ 6 }x-10 \\[1 em]y ~&=~ -\frac{ 5 }{ 6 }x + 4 \end{aligned} $$