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