Check perlop. '?:' has higher precedence than '=', so your code is equivalent to:

(
 ($key eq "year")
 ? &show($bros->{$data}->[$list])
 : $index
) = 0;
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And since you didn't want to return any value (not even an lvalue) from the '?:' operator, you would have been better off using a conventional if (...) {...} else {...} construct. Using '?:' in a void context can be confusing to a maintenance programmer.