puzzle vs think over

puzzle is a noun but think over is not a noun.

Word	Noun	Adjective	Verb	Adverb
puzzle	Yes	No	Yes	No
think over	No	No	Yes	No

As verbs, think over is a hypernym of puzzle; that is, think over is a word with a broader meaning than puzzle:

puzzle: be uncertain about; think about without fully understanding or being able to decide
think over: reflect deeply on a subject

puzzle (noun)	think over (noun)
a game that tests your ingenuity
a particularly baffling problem that is said to have a correct solution

puzzle (verb)	think over (verb)
be a mystery or bewildering to	reflect deeply on a subject
be uncertain about; think about without fully understanding or being able to decide