To solve this problem, we need to simplify the expression step by step:

First, subtract the second quantity from the first quantity:
(19 - 8 7/8) - (4 5/6 - 2 8/9)

Perform the subtraction within each quantity separately:
(19 - 8 7/8) = 19 - (8 + 7/8) = 19 - 8 - 7/8 = 11 1/8

(4 5/6 - 2 8/9) = 4 + 5/6 - (2 + 8/9) = 4 + 5/6 - 2 - 8/9 = 2 1/6 - 8/9

Find a common denominator for the fractions:
(2 1/6 - 8/9) = (2 9/9 + 1 9/9) - 8/9 = (18/9 + 1/9) - 8/9 = 19/9 - 8/9 = 11/9

Finally, subtract the two simplified quantities:
11 1/8 - 11/9 = (99/8) - (88/9)

Find a common denominator for the fractions:
(99/8) - (88/9) = (99 9/9 8) - (88 8/8 9) = (891/72) - (704/72)

Subtract the fractions:
(891/72) - (704/72) = (891 - 704) / 72 = 187 / 72

Therefore, the result of the expression (19-8 7/8)-(4 5/6-2 8/9) is 187/72 or 2 43/72.