Are "claw hammer", "ball- hammer", and "sledgehammer" proper nouns in this sentence.

"There are many types of hammers, the claw hammer, the ball- hammer, and the sledgehammer."

Because in the instructions for my homework, it says specific things, or examples are proper nouns, but when I did some research it says that proper nouns are always capitalized, so I am a bit confused.

No.

Proper nouns have capital letters at the beginning because they are formal names or titles.
San Francisco
James Stewart
St. Louis, Missouri
Pope John Paul XXIII

http://grammar.ccc.commnet.edu/grammar/nouns.htm
A proper noun, which names a specific person, place, or thing (Carlos, Queen Marguerite, Middle East, Jerusalem, Malaysia, Presbyterianism, God, Spanish, Buddhism, the Republican Party), is almost always capitalized. A proper noun used as an addressed person's name is called a noun of address. Common nouns name everything else, things that usually are not capitalized.

Those are common nouns. My claw hammer is the same as my neighbor's, yours, and those in the hardware store.

Please discuss this with your teacher. The text is not teaching correct things, and your teacher should have caught this.

In the given sentence, "claw hammer," "ball- hammer," and "sledgehammer" are not proper nouns. Proper nouns are specific names of people, places, or things, and they are typically capitalized.

In this case, the terms "claw hammer," "ball- hammer," and "sledgehammer" are not specific names of individual hammers; instead, they describe different types or categories of hammers. These terms are common nouns rather than proper nouns. Common nouns are general names for people, places, or things, and they do not need to be capitalized unless they start a sentence.

To answer your question, the words "claw hammer," "ball- hammer," and "sledgehammer" are not proper nouns in the given sentence.