First, let's simplify the expressions:

6 - 7 1/8 = 6 - 57/8 = 48/8 - 57/8 = -9/8

2/9 + 2/3 = 2/9 + 6/9 = 8/9

Now, we multiply the simplified expressions:

(-9/8) × (8/9) = (-9/1) × (1/1) = -9

Therefore, the final answer is -9.