Since the coins are distinguishable so we can speak of the first coin and the second coin. Since either coin can turn up Head (H) or Tail (T), the possible outcomes may be
Heads on both the coins = (H,H) = HH
Head on first coin and Tail on the other = (H,T) = HT
Tail on first coin and Head on the other = (T,H) = TH
Tail on both coins = (T,T) = TT
Combination of all the above outcomes will give us the sample space
Thus, the sample space is S = {HH, HT, TH, TT}