In this question are two important lines
(1)Color pairs used to color any two letters are different- Means Say (A,A) is painted with (c1,c2) and (B,B) is painted with (c3,c4) then it should not be the case for any such letter pair that (c1=c3 and c2=c4).
(2)Both prints of a letter can be colored with same color- Means (A,A) can be colored using single color also say c1.
Now, since options are given, we start with minimum possible option that is 6.
First, since pairs of Same letter can go with 1 color, A-F pairs are colored with 6 colors C1-C6.
Now using 6 colors, we can form 6C2=15 pairs which can further be used to color the letter pairs from (GG) to (UU)
Now we have exhausted all ways in which we can use 6 colors to paint our letterbook, but still some letters are remaining (5 of them)
Using one extra color, say C7, we can form 6 new color pairs from existing colors C1-C6
(C1,C7),(C2,C7).......(C6,C7)- 6 of new color pairs.
5 pairs of letters can be colored with this.
Hence, we need only 7 colors.