To simplify this expression, we need to follow the order of operations.

Start with the innermost parentheses:
1/2 + 2/3 = (3/6 + 4/6) = 7/6 or 1ц1/6

Next operation in the innermost parentheses:
1ц1/6 ÷ 3 = (4/6 ÷ 3/1) = (4/6 * 1/3) = 4/18 or 2/9

Combine the above results with the remaining terms in the expression:
1/4 + 2/9 = (9/36 + 8/36) = 17/36 or 1ц17/36

Divide by 3/4:
(17/36 ÷ 3/4) = (17/36 * 4/3) = 68/108 or 17/27

Subtract 2/3:
17/27 - 2/3 = (17/27 - 18/27) = -1/27

Divide by 8/9:
(-1/27 ÷ 8/9) = (-1/27 * 9/8) = -9/216 or -1/24

Therefore, the result of the expression 2:1/4+((1ц1/2+2ц2/3):3ц3/4-2/3):8ц8/9 is -1/24.