To simplify the expression, we first need to perform the operations within each fraction.

6 3/4 ÷ 9 = 27/4 ÷ 9 = 27/4 * 1/9 = 27/36 = 3/4

24 ÷ 6/7 = 24 * 7/6 = 168/6 = 28

1/9 ÷ 4/21 = 1/9 * 21/4 = 21/36 = 7/12

Now we substitute these results back into the expression:

3/4 + 28 - 7/12
= 9/12 + 28 - 7/12
= 32 - 7/12
= 384/12 - 7/12
= 377/12

Therefore, the simplified expression is 31 5/12.