This one is a bit tricky as you need to figure out the number of flashes for each of the letters first.
However, it is actually easier than you think.
The first two letters only require one flash each. There are only two lights, Red and Blue. So there can only be two combinations of single flashes.
The next four letters require two flashes each. There can be four combinations of two flashes: RB, RR, BR, BB. So this will cover C, D, E and F
There can be eight combinations of three flashes: RRR, BRR, RBR, RRB, BBB, BBR, RBB, BRB.
So this will cover G, H, I, J, K, L, M and N.
For the remaining 12 letters, four flashes will be required.
Since each flash takes one second, total number of seconds:
(1 x 2) + (2 x 4) + (3 x 8) + (4 x 12) = 2 + 8 + 24 + 48 = 82 seconds
Between each of the 26 letters, there will be 25 one second gaps. So time for gaps = 25 x 1 = 25 seconds
Total number of seconds = 82 + 25 = 107 seconds