To solve this expression, we first simplify each set of parentheses separately:

(-12/5 + (-3.6))
-12/5 + (-3.6) = -12/5 - 18/5 = -30/5
= -6

(-2 5/6 + (-2/3))
-2 5/6 + (-2/3) = -17/6 + (-2/3) = -17/6 - 4/6 = -21/6
= -7/2

Now, we add the results of the two simplified expressions:
-6 + (-7/2) = -6 - 7/2 = -12/2 - 7/2 = -19/2
= -9.5

Therefore, (-12/5 + (-3.6)) + (-2 5/6 + (-2/3)) simplifies to -9.5.