The author's use of syntax in this passage begins with__________ and follows with________________, ending finally...

I am not sure which specific example of syntax you need to
analyze, but your instructor appears to be asking you to analyze the parts of speech or
the use of a variety of independent and dependent clauses.  If you are looking at a
paragraph, it may be that you are being asked to look at the types of sentences that are
put together to create that paragraph.

Here is an example
of how you could complete your sentence using the following made up sentence:  The young
man left the dog at the shelter, hoping for the best.

The
author's use of syntax in this passage begins with a simple subject (the
young man) and follows with the verb and direct object,
followed by a prepositional phrase which explains where he left the dog,
and ends with a participle phrase which functions as an
adjective describing the young
man.

If you are being asked to
analyze a paragraph, you should look at what types of sentences are being used (simple,
compound, compound-complex).  You would also want to consider rhetorical strategies such
as periodic sentences, antithesis, parallelism, etc.

If you
scroll down through the link below you will find other links to a variety of terms
associated with a discussion of syntax.  This may help you find the appropriate language
to complete your assignment.