What is the rule of an input of -2 and an output 4?

If by 'rule' you mean 'function' then there are an infinite number of possible answers. However, here are some examples. (Let input be x and output y.) Linear Functions y = x + 6 y = 3x + 10 Polynomials y = 3x2 - x - 10 y = x4 + 2x3 + 3x2 - 2x - 12 Exponentials y = 0.5x