To simplify the given expression, we first need to evaluate the trigonometric functions for the given angles.

From trigonometric identities, we know that:

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

Now, let's substitute these values into the expression:

2(sin^2(-π/6) + cos^2(-π/3))/(2cos(-π/3) + sin(-π/6))

= 2[(-1/2)^2 + (√3/2)^2]/[2(1/2) + (-√3/2)]

= 2[(1/4) + (3/4)]/[1 + (-√3)]

= 2(1)/[1 - √3]

= 2/[1 - √3]

Therefore, the simplified expression is 2/(1 - √3).