To add the fractions 6/19, 7/8, and 2 5/8, we first need to convert the mixed number 2 5/8 to an improper fraction.

2 5/8 = (2 * 8 + 5)/8 = 16/8 + 5/8 = 21/8

Now, add the fractions:

6/19 + 7/8 + 21/8

To add these fractions, we need to find a common denominator. The least common multiple of 19, 8, and 8 is 152.

Therefore,

6/19 = (6 * 8)/152 = 48/152
7/8 = 91/152
21/8 = 189/152

Now, add these fractions:

48/152 + 91/152 + 189/152 = 328/152

Now, simplify the fraction:

328/152 = 164/76

Therefore, the sum of 6/19, 7/8, and 2 5/8 is 164/76.

Finally, subtract 4 6/19 from this result:

164/76 - 4 6/19

First, convert 4 to an improper fraction:

4 = 4/1

Now, subtract the fractions:

164/76 - 4 6/19 = 164/76 - 4 - 6/19

Find a common denominator of 76 and 19, which is 76:

164/76 - 304/76 - 24/76

Now, subtract:

(164 - 304 - 24)/76 = -164/76 = -82/38

Therefore, the result of the operation is -82/38 or -41/19.