First, let's simplify the expression inside the parentheses:

1/6 + 1 1/3 = 1/6 + 4/3
= 1/6 + 8/6
= 9/6
= 3/2

Now the expression becomes:

0.625 - 2 7/8 * 3/2

Now let's convert 2 7/8 to an improper fraction:

2 7/8 = 23/8

Now we multiply 23/8 by 3/2:

23/8 * 3/2 = 69/16

Now the expression becomes:

0.625 - 69/16

Now we need to convert 0.625 to a fraction:

0.625 = 625/1000 = 5/8

Now the expression becomes:

5/8 - 69/16

To subtract the fractions, we need a common denominator, which is 16:

5/8 = 10/16

Now the expression is:

10/16 - 69/16 = -59/16

Therefore, 0.625 - 2 7/8 * (1/6 + 1 1/3) = -59/16.