Hello there. To solve this question, we have to remember some properties about conjugates and real (complex) numbers.
Suppose the expression

Is a real number, hence we know that

must also be a real number because the real numbers are a field and they are closed under addition.
The conjugate of a real number is then the real number itself, which means that

Otherwise, if y is a complex number, it means it's imaginary part is not equal to zero.
Assuming y = a + bi for a, b real numbers and b not equal to zero, we have that

Hence the conjugate of this number is

That is equivalent to have

If y is a complex number.