決してあなたを忘れません。

never; by no means; not in the least; in no way

you (referring to someone of equal or lower status); dear (what a wife calls a husband)

indicates direct object of action; indicates subject of causative expression; indicates an area traversed; indicates time (period) over which action takes place; indicates point of departure or separation of action; indicates object of desire, like, hate, etc.

to forget; to leave carelessly; to be forgetful of; to forget about; to forget (an article)