* The - This is a definite article, not a noun.
* quick - This is an adjective, not a noun.
* brown - This is an adjective, not a noun.
* fox - This is a noun, referring to an animal.
* jumps - This is a verb, not a noun.
* over - This is a preposition, not a noun.
* lazy - This is an adjective, not a noun.
* dog - This is a noun, referring to an animal.
Therefore, there are two nouns in the sentence: fox and dog.