理解, 納得, and 同意: understanding, accepting reasons, and agreeing
Compare understanding how a machine works, accepting a decision after hearing reasons, and agreeing to a meeting-place change. These are not mandatory successive stages.
Understanding content or a mechanism
理解 (りかい) means understanding or comprehension. 「図解を読むと、機械が動く仕組みを理解しやすくなります。」 says reading a diagram makes the machine’s mechanism easier to understand.
「文化の違いを理解するには、相手の話をよく聞くことが大切です。」 says listening carefully to the other person is important for understanding cultural differences. Ease or an important method does not establish completed understanding.
Accepting a reason or judgment
納得 (なっとく) concerns accepting reasons or finding a judgment convincing. 「理由を聞いて、ようやく彼の判断に納得した。」 says the speaker finally accepted his judgment after hearing the reason.
「全員が納得できるまで案を練り直そう。」 proposes revising the proposal until everyone can accept it. It does not report that everyone already does.
Agreeing to a proposal or change
同意 (どうい) means agreement or consent. 「全員の同意を得て集合場所を変更した。」 says the meeting place was changed with everyone’s agreement.
「私はその提案に同意します。」 expresses agreement with that proposal. Understanding content, accepting reasons, and agreeing can be related without forming a required sequence of stages.
What was obtained and then changed in 「全員の同意を得て集合場所を変更した。」?
Show the answer and why
Everyone’s agreement was obtained, and the meeting place was changed. 同意 concerns agreement to the change, rather than merely understanding a mechanism or hearing reasons.