The term 'MAINTAIN THAT' can be broken down into two crossword solutions: ALLEGE (6 letters) and CONTEND (7 letters). To ALLEGE something is to make a claim without providing proof, while to CONTEND is to assert or maintain a position in an argument. Both words are used to express a belief or opinion, but the difference lies in the level of certainty. Alleging something implies that the speaker is not sure of its truth, while contending something implies that the speaker is more certain of its truth.