complete the square
get it to form
(x-h)²+(y-k)²=r²
r is radius
so
(x²+4x)+(y²-6y)-12=0
take 1/2 of each linear coefient and square it and add it to both sides
4/2=2, 2²=4
-6/2=-3, (-3)²=9
add 4+9 to both sides
(x²+4x+4)+(y²-6y+9)-12=9+4
factor
(x+2)²+(y-3)²-12=13
add 12 both sides
(x+2)²+(y-3)²=25
(x+2)²+(y-3)²=5²
radius is 5
3rd option