Advanced Custom Fields – display when specific template used?

Hard to give an exact answer without sharing your code, but using is_page_template() in an if statement will help determine when you display your custom field group:

if ( is_page_template( 'template-y.php' ) ) {
    # Display Field Group X code here...
}
else {
    # Do something else...
}

Again, if you could provide your code, I can give you a better answer.