Remember that you can only cross-reduce AFTER you FLIP and CHANGE the OPERATOR.
ORIGINAL PROBLEM: 2/9 ÷ 2/3 = FLIP and CHANGE OPERATOR: 2/9 * 3/2 = REDUCE (if possible): 1/3 * 1/1 = MULTIPLY: 1/3 * 1/1 = 1/3
ORIGINAL PROBLEM: 2/3 ÷ 3/4 = FLIP and CHANGE OPERATOR: 2/3 * 4/3 = REDUCE (if possible): 2/3 * 4/3 = MULTIPLY: 2/3 * 4/3 = 8/9
Now you get to try a few for yourself.