To simplify this expression, we will first distribute the coefficients:

-6(2/3a - 1/6) + 4(3/4a - 1/12)

Next, simplify the terms within the parentheses:

-6(2/3a - 1/6) = -6(2/3a) + 6*(1/6) = -4a + 1

4(3/4a - 1/12) = 4(3/4a) - 4*(1/12) = 3a - 1/3

Now we have:

-4a + 1 + 3a - 1/3

Combine like terms:

-4a + 3a + 1 - 1/3

Simplify:

-a + 1 - 1/3

Combine the constant terms:

-a + 2/3

Therefore, -6(2/3a - 1/6) + 4(3/4a - 1/12) simplifies to -a + 2/3.