Let's simplify the expression:

-0.5(2y-0.6) + 2(-0.15 - 1/3y)
= -1y + 0.3 + (-0.3 - 2/3y)
= -1y + 0.3 - 0.3 - (2/3)y
= -y - (2/3)y
= -1y - (2/3)y
= -1y - 2/3y
= -(3/3)y - 2/3y
= -5/3y

Therefore, the simplified expression is -5/3y.