a new hot has 32 rooms on the second floor. then rooms will be numberesd 201 to 232. the manaher wants to puit brass numerals on the door of each room how many number 2s will be needed

each room number starts with a 2, so 32 for the lead digit.

middle digit:
220 - 229 ---> 10 2's
unit digit:
202,212,222, 232-->4 2's

total 2's : 32+10+4 = 46

(please proof-read you question, it is riddled with spelling and grammar errors)