The distance between points $ A $ and $ B $ is :
$$ d(A, B) = \sqrt{ 181 } $$To find distance between points $ A(x_1,y_1)$ and $ B(x_2,y_2)$, we use formula:
$$ \color{blue}{ d(A,B) = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} } $$In this example we have:
$$ \begin{aligned} & A \left(4,~-6\right) \implies x_1 = 4 ~~\text{and}~~ y_1 = -6 \\[1 em] & B \left(13,~4\right) \implies x_2 = 13 ~~\text{and}~~ y_2 = 4 \end{aligned} $$Substituting $ x_1 $, $ x_2 $, $ y_1 $ and $ y_2 $ into the formula above yields:
$$ \begin{aligned} d(A,B) & = \sqrt{\left( 13 - 4 \right)^2 + \left( 4 - \left( -6\right) \right)^2} \\[1 em] d(A,B) & = \sqrt{ 9^2 + 10^2 } \\[1 em] d(A,B) & = \sqrt{ 81 + 100 } \\[1 em] d(A,B) & = \sqrt{ 181 } \\[1 em] d(A,B) & = \sqrt{ 181 } \end{aligned} $$