Question

What would be the value of g on the earth if its mass was twice as large and its radius half of what it is now?

Answer 1

8 times because F = m1g =Gm1m2/r^2
g = Gm1/r^2 ..and it is given that mass is twice and radius is half then by following last equation the value of g is becomes 8 times

Answer 2

Therefore, G would be eight times larger, since it is proportional to mass and inversely proportional to the distance squared.
The earth would need to be 16 times as dense, though, which is quite impossible. The density of rock is around 3 g/cm^3, of iron around 8 the 'Earth' overall around 6. The densest known material is around 22 g/cm^3, which is only roughly 4 times as much. Even when you consider increased compression, no planet could possibly satisfy your conditions, even if it were made of pure Osmium.