Answer: shown below
DS + ST = DT by the Segment Addition Postulate. So, we can substitute and find X.
(2x - 8) + (3x - 12) = 60
2x - 20 + 3x = 60
5x - 20 = 60
5x = 80
x = 16
We can double check and use this to find DS and ST.
DS = 2(16) - 8
DS = 32 - 8
DS = 24
DT = 3(16) - 12
DT = 48 - 12
DT = 36
24 + 36 = 60, so X is 16.