To solve this expression, we must first simplify each fraction and then perform the operations in the correct order.

19ц - 15ц4\7 = 19ц - 15 * 7 + 4 = 19ц - 105 + 4 = 19ц - 101.

Next, we have:

(19ц - 101) : 16\21 + 6ц 3\5 - 4ц 5\6

To simplify the division, we multiply by the reciprocal:

(19ц - 101) * 21\16 + 6ц 3\5 - 4ц 5\6

(19ц 21\16) - (101 21\16) + 6ц 3\5 - 4ц 5\6

399ц\16 - 2121\16 + 6ц 3\5 - 4ц 5\6

Now distribute the fractions to the ц terms:

399ц\16 - 2121\16 + 6ц\5 + 3 - 4ц\6 - 5

Combine the ц terms:

(399\16 - 2121\16 + 6\5 - 4\6)ц + (3 - 5)

Simplify the fractions first:

(399 - 2121 + 96 - 40)\16ц - 2

Now combine the numbers:

( -1626 )\16ц - 2

-1626\16ц - 2

Now simplify the fraction:

-101ц 5\8 - 2

Therefore, the final answer is -101ц 5\8 - 2.