You need to show the relationship between x and y in order to establish the domain and range. You have provided an expression rather than an equation, so the question is not complete. If, for instance, you had 2x+4y=5, then you have established a relationship between x and y, and the domain (the set of values that x can take) and the range (the resulting values of y) can be worked out.
As it stands, f(x,y)=2x+4y is an equation of two independent variables resulting in a third quantity which is dependent on both of them. So the domain would be all (real) values of x and y, and the range would be infinite, because x and y are unrestricted and unconstrained.