あなたの後ろのドアをしめて下さい。

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

indicates possessive; nominalizes verbs and adjectives; substitutes for "ga" in subordinate phrases; (at sentence-end, falling tone) indicates a confident conclusion; (at sentence-end) indicates emotional emphasis; (at sentence-end, rising tone) indicates question

back; behind; rear

door (Western-style)

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 make; to let

to give; to confer; to bestow; to kindly do for one; to oblige; to favour; to favor