We are given the coordinates of the center and one point of a circle. To determine the radius we must determine the distance between the two points. To do that we will use the following formula:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Where:
[tex]\begin{gathered} (x_1,y_1)=(0,4) \\ (x_2,y_2)=(-6,4) \end{gathered}[/tex]Replacing in the formula for the distance:
[tex]d=\sqrt[]{(-6-0)^2+(4-4)^2}[/tex]Solving the operations:
[tex]\begin{gathered} d=\sqrt[]{(-6)^2+0^2} \\ d=\sqrt[]{36} \\ d=6 \end{gathered}[/tex]Therefore, the radius of the circle is 6.