∵|a-2|+(b+3)²=0
∴a-2=0,b+3=0
∴a=2,b=-3
∴3a²b-[2ab²-2(ab-1.5a²b)+ab]+3ab²
=3a²b-[2ab²-2ab+3a²b+ab]+3ab²
=3a²b-2ab²+2ab-3a²b-ab+3ab²
=ab²+ab
=ab(a+b)
=2×(-3)(2-3)
=-6×(-1)
=6