To solve this expression, we can simplify each term separately and then add them together.

First term:
3/10 (-5/6)
= 3(-5)/(10*6)
= -15/60
= -1/4

Second term:
2/3 (-3/8)
= 2(-3)/(3*8)
= -6/24
= -1/4

Now we add the two simplified terms together:
-1/4 + (-1/4)
= -1/4 - 1/4
= -2/4
= -1/2

Therefore, 3/10 (-5/6) + 2/3 (-3/8) simplifies to -1/2.