A synthesis paper combines multiple cited sources in a cohesive and clear analysis and explanation. The objective in question is not a noun but rather an adjective. That is, there is not "an objective" involved. Rather, the paper is meant to be objective. Instead of a subjective paper in which you introduce your own opinion, an objective synthesis paper explains the ideas of others in your own words.

Being Objective

Though it might be tempting to introduce your own viewpoint, the purpose of a synthesis paper is to teach you to synthesize and cite different or opposing ideas in a balanced manner. Do not describe the viewpoints and sources addressed in your paper with words that carry positive or negative correlations. Be careful to avoid value judgments that identify any viewpoint with a superior or more persuasive perspective. The goal is to show that you understand and articulate more than one perspective while showing how the disparate sources relate to each other.