Assignment rhymes with:
reassignment, consignment, reassignment, alignment, confinement, consignment, realignment, reassignment, refinement, abandonment, adjournment, adornment, alignment, apportionment, arraignment, atonement, attainment, confinement, consignment, containment, discernment, disillusionment, enlightenment, entertainment, environment, imprisonment, infotainment, internment, misgovernment, nongovernment, postponement, realignment, reapportionment, reassignment, refinement, self-government
Assignment sounds like:
acantha, accent, accented, accentuate, accentuated, accomando, accommodate, accommodated, account, accounted, achmed, acmat, acquaint, acquainted, agenda, agent, agneta, ajinomoto, aksamit, aquanaut, ascend, ascended, ascent, ashamed, ashmead, assante, assassinate, assassinated, assent, assessment, assigned, assumed, augment, augmented, ausimont, awakened