Learn Finnish: Älä käytä näitä hammastahnoja!

näitä is the partitive plural form of the demonstrative pronoun tämä (this). In this sentence, the verb käyttää (to use) forces its object into the partitive case. Since we are talking about plural "toothpastes", both the pronoun and the noun must be in the partitive plural.

Why is the verb form just käytä?

This is a negative command ("Do not use"). To tell one person not to do something, you use älä followed by the verb's stem. The verb is käyttää, and its stem is käytä. Notice that the two T's drop to one T because of consonant gradation.

If commands sometimes drop the object's case ending, why does hammastahnoja still have a partitive ending here?

It is true that positive commands often take a nominative (basic form) object. However, käyttää is a partitive verb, meaning its object is almost always in the partitive. On top of that, negative commands like älä käytä always require their object to be in the partitive case anyway.

How do you form the partitive plural hammastahnoja from the basic word?