* alligator: This is a noun. It's the name of a creature.
* Florida: This is an adjective. It modifies the noun "alligator" to specify what kind of alligator we're talking about.
* and: This is a conjunction. It connects two words or phrases ("alligator Florida" and "armadillo").
* armadillo: This is another noun. It's the name of a different creature.
So, the parts of speech are: noun, adjective, conjunction, noun.