To simplify the expression 1/6a × 8b² × 3/4ba³ with a = -2 and b = 1/2, we substitute the values of a and b into the expression:

1/6(-2) × 8(1/2)² × 3/4(-2)(1/2)³
= -1/3 × 8(1/4) × 3/4(-1)1/8
= -1/3 × 2 × 3/4 × (-1)/8
= -2 × 3/4 × (-1)/8
= -6/4 × (-1)/8
= -3/2 × (-1)/8
= 3/2 × 1/8
= 3/16

Therefore, the simplified expression is 3/16.