i dont know how to solve and check

(x-2)^(2/3) =  36   raise  both sides to the  3/2   power

[ (x - 2) ^(2/3) ]^(3/2)   =  36 ^(3/2)

(x - 2)^(2/3 * 3/2)  =  ( √ [ 36] )^3

(x - 2) ^1   =  (6)^3

x - 2 =  216     add 2 to  both sides

x   = 218

Check

(218 - 2)^(2/3)   =36   ???

(216)^(2/3)  = 36  ???

[ (216)^(1/3) ] ^2  = 36  ???

[ ∛216] ^2  = 36  ???

[6]^2   = 36        true   !!!!