Agrouping of words that acts like a single unit inside a sentence but that does not contain both a subject and a verb is called a(n)
a. clause.
b. phrase.
c. apostrophe.
d. compound sentence.

The answer is letter B-- phrase.

A phrase referes to a group of words that act as one 
unit or a single part of speech in a sentence. It doesn't have both a subject and a verb, yet it acts as either a subject or a verb. It's a part of a sentence which doesn't express a complete thought. 

For example:

The beautiful house down the road is owned by my teacher.

The noun phrase is-- The beautiful house down the road
The verb phrase is-- owned by my teacher

These are the phrases of these sentences which cannot stand alone. 

Objective pronoun is the answer.