Enhancement rhymes with:
advancement, financement, advancement, announcement, announcment, commencement, financement, pronouncement, advancement, announcement, announcment, assessment, basement, bemusement, commencement, debasement, disbursement, displacement, embarrassment, emplacement, endorsement, enforcement, engrossment, enticement, financement, harassment, impressment, inducement, osment, outplacement, placement, pronouncement, reassessment, reimbursement, reinforcement, replacement, retracement
Enhancement sounds like:
enchant, enchanted, engagement, engined, enjoined, enjoyment