If C = 9 and DOG = 78 then how will you code BAT?

Each letter is first replaced by its position in the English alphabet (A = 1, B = 2, ... Z = 26). The position values of all the letters in a word are added together, and that sum is then transformed by one fixed rule -- the same rule that must hold for every given example -- to produce the word's code.

1. Find the rule from the single-letter example: C is the 3rd letter, so its position value is 3. The given code for C is 9, and 3 x 3 = 9, so the rule appears to be "position-sum x 3".

2. Confirm the rule with the three-letter example: D = 4th letter, O = 15th letter, G = 7th letter, so D + O + G = 4 + 15 + 7 = 26. Applying the rule, 26 x 3 = 78, which matches the given code for DOG -- this confirms the rule.

3. Apply the confirmed rule to BAT: B = 2nd letter, A = 1st letter, T = 20th letter, so B + A + T = 2 + 1 + 20 = 23. Applying the same rule, 23 x 3 = 69.

Both given examples (C -> 9 and DOG -> 78) are satisfied by exactly the same rule, position-sum x 3, so applying it to BAT is not a coincidence of just one example. Reversing the final step, 69 / 3 = 23, which is exactly B + A + T's position-sum, confirming the working.

So BAT is coded as 69.