Time expressions can be tricky to use with apostrophes. Day’s, days’, and days are in fact all correct depending on the context.
Days is used for the plural of day. Day’s and days’ are used in compound time expressions. Day’s is used with a singular time unit and days’ is used for a plural when day is possessive.
Day’s and Days’
One day’s experience
Two days’ experience
You need to place the apostrophe before the s when you are writing about a singular time(one day, one month, one year) and after the s when it is a plural time(two days.Three days, four days)
Notice that we only need to do this when we include the noun that the time expression is about(possessive). We only do this when we can replace the apostrophe with of.(Read about when to use of in English grammar here).
One day’s free entry
Four days’ free entry
She is going away in one day’s time.
She is going away in two days’ time.
He was docked one day’s pay.
He was docked two days’ pay.
You can always use “of” if you feel like this makes things clearer:
He was docked one day of pay.
He was docked two days of pay.
In this case, “days” returns to a regular singular/plural noun.
If there is no noun that the time expression is connected to then “days” acts like a regular noun and you just need to add an s to make it plural.
I need to start work in one day.
I need to start work in two days.
Compound adjectives with day
Compound adjectives are when we combine two words with a hyphen to describe another noun.
He took a two-day trip.
The package includes a one-day safari.
For compound adjectives, it is not necessary to add an s, but it is necessary to add the hyphen.