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each statement alone is not sufficient, i think that's clear enough because this is one linear equation with two variables - not a big of a constraint. for example, take x=4 y=1 or y=-1, both satisfy statement 1, but give different answers to the question.
however, both statement are sufficient. there are several ways to get there, here is one:
x-y>-2 and x-2y<-6. if x-y>-2 and you take y out (to get x-2y) and get a number less than -6 it must be that y>4. (you could solve the equations, but i prefer not to).
now, if y>4 then from x-y>-2 => x>y-2 => x>2
so both x and y are positive ance xy>0
b.t.w to solve the equation youo should rewrite statement 2:
x-2y<-6 => 2y-x>6.
then add the two statements to get y>4.