Your two examples are correct. # years old comes after a verb. "I will become 20 years old." #-year-old comes before a noun. I have a six-year-old son.

The child is three years old. = Complete sentence The child = subject is three years old = predicate The three-year-old child....= part of a sentence that need completing The = article three-year-old = adjective child = noun Actually the difference is quite obvious.

There is no difference in meaning really... the difference is rather the placement of the adjective, which becomes compounded (or hyphenated) when it goes before the verb. This often happens in English when an adjective has more than one word, which is to say, when it is an "adjectival phrase."... Examples: "The dragon with five heads." = "The five-headed dragon..." "The girl with short hair." = "The short-haired girl...." This is done for clarity in sentences where the adjective is followed by another verb expressing more information or action.

The child is three years old.....................matter is about the age of a child. The three year old child...........................matter is about a child which has three years.