To simplify the expression 6cos(π/3) - 2sin(-π/6), we need to know the values of cosine and sine of the angles π/3 and -π/6.

cos(π/3) = 1/2
sin(-π/6) = -sin(π/6) = -1/2

Now we can substitute these values into the expression:

6cos(π/3) - 2sin(-π/6)
= 6(1/2) - 2(-1/2)
= 3 - (-1)
= 3 + 1
= 4

Therefore, 6cos(π/3) - 2sin(-π/6) simplifies to 4.