The Reduce code from @BillNelson explicitly allows for variables to take on all values between 0 and 1 inclusive.
Reduce
The values the 4 variables can take are not just 0 or 1. They can take any value between 0 and 1, like 0.001, 0.002,,..... 0.999 etc. So there are actually a large number of alternatives here.
Try
Reduce[{0<=a<=1,0<=b<=1,0<=d<=1,0<=gamma<=1,(-2a+2b-2d+4a gamma-4b gamma+4d gamma)/ (-3a+2b-3d+6a gamma-6b gamma+6d gamma)<6/10},{a,b,d,gamma}]
Please check all this very carefully to understand how it works and see if I have made any mistakes.
