#32÷(6-2sqrt5)#
means
#32/(6-2sqrt5)#
multiply by the conjugate
#32/(6-2sqrt5)*(6+2sqrt5)/(6+2sqrt5)#
#color(red)((6-2sqrt5)*(6+2sqrt5) = 6^2 - (2sqrt5)^2=36-20 = 16)#
#color(red)("difference of two sequares")#
#(32*(6+2sqrt5))/ 16#
#color(red)(32/16 = 2)#
#2*(6+2sqrt5) = 12+4sqrt5#