ABCE : BCEG : : ? : EGKM

The pattern in the given analogy is as follows:

• ABCE : BCEG :: ? : EGKM

In the first pair, each letter in the second term is two places ahead of the corresponding letter in the first term in the English alphabet.

• A (1st letter) -> B (2nd letter)
• B (2nd letter) -> C (3rd letter)
• C (3rd letter) -> E (5th letter)
• E (5th letter) -> G (7th letter)

So, the missing term should be two places behind each letter in the term EGKM in the English alphabet.

• E (5th letter) -> C (3rd letter)
• G (7th letter) -> E (5th letter)
• K (11th letter) -> I (9th letter)
• M (13th letter) -> K (11th letter)

So, the missing term is CEIK.

Therefore, the complete analogy is:

• ABCE : BCEG :: CEIK : EGKM