Here is me trying:
There are 6 letters, right? All of them are different. You make a tree diagram or a chart.
There are this many: FA, FB, FR, FI, FC, AF, AB, AR, AI, AC, BF, BA, BR, BI, BC, RF, RA, RB, RI, RC, IF, IA, IB, IR, IC, CF, CA, CB, CR, CI.
That is if the same letter cannot be used twice within one permutation. If that can happen, then add 6 to the number.
My answer: 30