Is 2xy=-8 a function ?

Technically no, it is an equation. A function would be of the form: f(y)= (-8) / (2x). It is basically the same thing but written differently yet if you want to be accurate with the terminology, your answer is no.

It's like discovering the answer to a puzzle. the purpose in solving an equation is to find the value or values of the variable that makes it a true statement. any value of the variable that makes the equation true is called a solution to the equation.