(x-2):5 = 2:3-(3x-2):6

(x-2):5 = 2:3-(3x-2):6

(x-2)/5 = 2/3 - (3x-2)/6

(x-2)/5 = 2/3 - (3x-2)/6

6(x-2) = 10 - 5(3x-2)

6x - 12 = 10 - 15x + 10

6x - 12 = 20 - 15x

21x = 32

x = 32/21