To simplify the expression 7cos(π/4) - 6sin(π/2) - 2/3cos(-π/3), we first need to find the exact values of cosine and sine for the given angles.

cos(π/4) = √2/2
sin(π/2) = 1
cos(-π/3) = cos(π/3) = 0.5

Substituting these values into the expression, we get:

7(√2/2) - 6(1) - 2/3(0.5)
= (7√2)/2 - 6 - 1/3
= (7√2)/2 - 18/3 - 1/3
= (7√2)/2 - 19/3

Therefore, the simplified form of the given expression is (7√2)/2 - 19/3.