How can i effectively analyse the x bar theory of syntax in linguisticsThis is a language question

The X-bar theory is used when performing syntactic
analysis on a phrase or sentence usually in the form of a syntactic tree.  Essentially
what this theory states is that there are syntactic features that are common to all
human languages, one structural similarity of which is the
"x-bar"

Essentially what you do is use X as an arbitrary
lexical category, which can later become an N, V, A, or P (noun, verb, adjective,
preposition respectively).  The rules of X-bar theory are as
follows:

1. An X Phrase consists of an optional specifier
and an X-bar, in any order:
2. One kind of X-bar consists of an X-bar and an
adjunct, in either order:
3. One kind of X-bar consists of an X-bar and an
adjunct, in either order:

Applying these rules we can know
that:

A sentence is always composed of a noun phrase, and a
verb phrase (rule two).
A verb phrase is always composed of a verb and a
complement (rule 3).
A noun phrase can be composed of adjective phrases, and
must contain a noun (rule one).
Prepositional phrases must contain a
preposition and a noun phrase (rule one).
The same goes for adverb
phrases.