He makes sure he spends a few hours quality time with his children every day.
I've been thinking about your question here, Tony, and it seems to me that a good argument can be made for not using an apostrophe after hours.
I agree with Bazza's intuition that there is an ellipsis, or omission, of of in that example. The sentence is equivalent to He makes sure he spends a few hours of quality time with his children every day. If there is that ellipsis, then no apostrophe is needed.
There is a difference, after all, between speaking of a couple of weeks (of) vacation (time) / two weeks (of) vacation (time) and a two week's vacation. The former expressions focus on a quantity of vacation time, the latter on a type of vacation (a two week's vacation).
Are you aware that you have two weeks vacation time saved up? (no apostrophe; of is elided)
How did you spend your two week's vacation? (apostrophe; no ellipsis)
In the Cambridge dictionary example you have quoted, Tony, a few hours is a quantifying expression. It would be silly to say that the sentence is equivalent to this: (?)He makes sure he spends a three-hour quality time with his children every day. Yet I believe that's what the sentence would technically mean with an apostrophe after hours.
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