Correlation between two set of variables

Hello, i have a problem with a correlation study. I have to study the linear relationship between two set of variables X and Y. There are 12 variables in X and 4 in Y.

I applied a Canonical Correlation Analysis and it seemed all the variables in X with 3 in Y were correlated.

I also did a Kendall's test for each pair of variables (X,Y). I found out the same results. But i don't know what to do after doing all of that to proove there's a correlation bewteen X and Y.

Thanks :)
Hello. The variables in X represent several optic tests in the light. And the variables in Y measurements we've done on the eyes. My compagny wants to know if there is a connexion between those two set of variables.