Can't figure out unknown operation This is a problem I had on a test, and I completely don't understand where the answer is coming from.
If the operation Φ is defined for all X and Y by the equation XΦY=2Y/3X, then 4Φ(2Φ3)= ?
The answer given was 3/2, and the explanation is that the equation becomes 4Φ(18/12)=4Φ3=18/12=3/2.
It seems to me like the answer should be 4Φ(2Φ3)=4Φ((3x2)/2x3))=4Φ(6/6)=4Φ1=(2x1)/(3x4)=1/6.
Which wasn't even one of the multiple choice answers.
So I'm obviously completely misunderstanding the problem; some one please help.

If you defined $\Phi$ here as it was defined on the test, then your calculation of $2\Phi3$ is correct. Then you have a minor slip: $4\Phi 1=\frac{2\cdot 1}{3\cdot 4}$.
