"IN"同 "ON'用在時間，日期及年份不懂怎麼樣用，請大家幫助...謝謝。 eg, IN the last week / On the last week那個是對的?

this week
last week
next week
the week before last
the week after next
every other week
以上都不用介系詞，當副詞用。

in the first/last week of April (在某個月時,用in)
on Friday of this week (在某星期時,用on)
in 1997 (在某一年時,用in)

同理:
this month
last month
next month
this year
next year
today
yesterday
the day before yesterday
等都不需要介系詞

on the third (day) of this month
on Monday (在星期幾時用on)
on the Monday after next

at six o'clock (在指小時時,用at)

in April (在某個月時,用in)
in a week ( 一周內)
in the morning
in the afternoon
in the evening
in the night
at noon
at midnight
at dawn
at sunrise
at sunset

請參見柯旗化<新英文法>pp.552~555表時間的介系詞用法

我來完整的解釋一下，免得掛一漏萬:
In用法i
1，一季:in summer 2,年或世紀:in 2016 3,一個歷史片段:in the middle ages 4,月份 In Feb 5,一天的某一部份:in the morning 6.未來固定表示方法:in the near future in a few minutes

On 用法i
1，天或曰期: on Sunday 2,特定的日子〈如國定假日)on chrismas day 3.長時間片語且含day這個字 on Monday morning

不用介詞:this evening 2 last night 3,e every evening 4,today 5,the day after tomorrow

所以本問題歸類在第3項不用介詞，答案即last week就好，此類時間名詞已演化成副詞使用，你也可以認定將介詞省略亦可，文法上較易解釋。