Learn English – When would you rather use one over the other

They are both correct.

I am a twenty-year-old student:

1. "20" and "year" are linked by the hyphen to create a single term ("20-year") that modifies "old."
2. "20-year" and "old" are linked by the hyphen to create a single term ("20-year-old") that modifies "student."

I am twenty years old:

1. "old" is a predicate adjective for "I." (as in "I am old.") As a single-word adjective for "I," it is not joined with a hyphen to the previous adjective, "years."
2. "years" modifies "old," and "20" modifies "year". "20" and "years" are not acting as a single adjective for "old," so they, too, do not need a hyphen.

The easy understanding:

If the adjective phrase serves as a single modifier before the noun (student, in the second sentence), it needs a hyphen (or hyphens, as in this case). Adjective phrases have no plural forms on the words forming them (the word year you asked). When you use a noun as an adjective (year-old), it must be singular. That's why there is no -s there.

If it is after the noun, it doesn't need a hyphen (or hyphens). When the same words (years) are used not as an single adjective, which means they modify the noun separately, the noun is plural. That's why there is an -s there (unless it's She is 1 year old).

Another example:

• The ceiling is ten feet high.
• The room has a ten-foot ceiling.

The word vacational doesn't exist in any Dictionary. Nor do we find it in any Grammar book.

Like many other nouns used as adjectives, the noun "vacation" can be used as an adjective. For examples:

1. Shimla is a beautiful vacation spot.

2. My parents are trying to buy a vacation home in Darjeeling.

3. I have got a vacation job.

4. We don't have any vacation days left.

5. Vacation season hasn't set in yet.

I think we can also say "Vacation Studies English Language School".

To sum up, when we usually use 'vacation' as an adjective, there's no point in using 'vacational' that doesn't exist or is rarely used.