I will give it a hand,
6 letters , 2 same, can be arranged in 6!/2 different ways. When 2 are together in 5! different ways. Then the ans should be 6!/2-5!=240 ways when there wil be AT LEAST one letter in between.
Prof, i think that you select the letters out of the remaining 4 different but shouldn't the permutations of these selections be considered?