The distance between points $ A $ and $ B $ is :
$$ d(A, B) = 13 $$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:
$$ \begin{aligned} & A \left(1,~-3\right) \implies x_1 = 1 ~~\text{and}~~ y_1 = -3 \\[1 em] & B \left(6,~9\right) \implies x_2 = 6 ~~\text{and}~~ y_2 = 9 \end{aligned} $$Substituting $ x_1 $, $ x_2 $, $ y_1 $ and $ y_2 $ into the formula above yields:
$$ \begin{aligned} d(A,B) & = \sqrt{\left( 6 - 1 \right)^2 + \left( 9 - \left( -3\right) \right)^2} \\[1 em] d(A,B) & = \sqrt{ 5^2 + 12^2 } \\[1 em] d(A,B) & = \sqrt{ 25 + 144 } \\[1 em] d(A,B) & = \sqrt{ 169 } \\[1 em] d(A,B) & = 13 \end{aligned} $$