This a simple fraction question. To divide ^{6}/_{7} by ^{2}/_{9} we can follow these steps which applies to any fraction:

Step 1. Cross multiply the two fraction as shown below:
6 2 6 x 9
- x - = -----
7 9 7 x 2
Step 2. Simplify the fraction:
6 x 9 3 x 9 27
----- = ----- = --
7 x 2 7 x 1 7
Step 3. If the resulting fraction is an improper fraction, simplify it
27 6
-- = 3 -
7 7
That is all!

So, ^{6}/_{7} by ^{2}/_{9} is equal to ^{7}/_{27} which is equal to 3 ^{6}/_{7}.