Decoding the Pattern: FAMILY to GBNJMZ

First, we need to determine the coding rule used to transform 'FAMILY' into 'GBNJMZ'. Let's compare the letters position by position:

• F is the 6th letter, G is the 7th letter. ( $6 + 1 = 7$ )
• A is the 1st letter, B is the 2nd letter. ( $1 + 1 = 2$ )
• M is the 13th letter, N is the 14th letter. ( $13 + 1 = 14$ )
• I is the 9th letter, J is the 10th letter. ( $9 + 1 = 10$ )
• L is the 12th letter, M is the 13th letter. ( $12 + 1 = 13$ )
• Y is the 25th letter, Z is the 26th letter. ( $25 + 1 = 26$ )

The pattern is a simple forward shift cipher, where each letter in the original word is replaced by the letter immediately following it in the alphabet (a +1 shift).

Applying the Coding Rule to GBNJMZ

Now, we apply the same +1 shift rule to the string 'GBNJMZ':

• G (7th letter) + 1 = H (8th letter)
• B (2nd letter) + 1 = C (3rd letter)
• N (14th letter) + 1 = O (15th letter)
• J (10th letter) + 1 = K (11th letter)
• M (13th letter) + 1 = N (14th letter)
• Z (26th letter) + 1 = A (1st letter, wrapping around the alphabet)

Combining these shifted letters gives us the coded string 'HCOKNA'.

Final Answer Determination

Based on the identified +1 shift pattern, 'GBNJMZ' is coded as 'HCOKNA'. This corresponds to Option A.