Why is it wrong to say " a child of six years old" and is possible to say "a six-year-old child"?

Example: My family consists of /is made up of/ is composed of two adults and two children, six years old and ten years old.
But: .... of a six-year-old child and a ten-year-old child?

Can you please recommend me a nice and convenient four-star accommodation in West Yellowstone which lies not too far from the park? Thank you for your help!!

There are several ways to say that, but "of" is used the least. It's not actually incorrect; it's simply awkward (has that extra, unneeded word).

... a child of six.

... a child who is six years old.

... a six-year-old child.

Or try this ...
My family is made up of two adults and two children, ages six and ten.

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Can you please recommend me<~~~delete "me" a nice and convenient four-star accommodation in West Yellowstone which lies not too far from the park? Thank you for your help!!

http://www.google.com/search?q=hotels+west+yellowstone+mt&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-US:official&client=firefox-a
Hotels marked with C, G, and D seem to be the closest ones to the park's west entrance. All would be interesting to investigate, but I'd focus on those three.

It is considered incorrect to say "a child of six years old" because it violates the proper order of adjectives. When describing age, the correct order is to use the numeral adjective (such as "six") before the hyphenated phrase (such as "year-old"). Therefore, the correct phrase would be "a six-year-old child."

For your accommodation recommendation in West Yellowstone, you can try using online travel websites or search engines to find convenient four-star accommodations in the area. Some popular options include Booking.com, Expedia, or TripAdvisor. Simply enter your destination as West Yellowstone and filter the results to show four-star accommodations. Additionally, you can read the reviews and check the provided map to ensure that the accommodation is located within a reasonable distance from the park.