might be wrong, but here goes:
g= lambda
since 8x = 2g
that means that 8 = 2g/x
which means that 12 = 6g/2x
so 6g/2x = 2x +3y + 4z
6g = 2x(2x + 3y + 4z)
6g = 1/2g(1/2g + 3g + 4z)
12g^2 -3.5g = 4z
10z = 4g
z = 2/5g
8/5g + 3.5g =12g^2
1.6g + 3.5g = 5.1g
5.1g/g
5.1 = 12g
go from there.. i think