You mustn't forget your promise.

Literal

Promise [obj-を] forget-[prohibition-てはいけない].

The classic prohibition pattern ~てはいけない ('must not X'). Plain form, contracting to ~ちゃいけない in casual speech. The underlying structure is literally 'even-doing X is no good' — the てはいけない unpacks as て (and/if) + は (topic) + いけない (won't do, is no good).