Which quality helps self-employed graphic designers sell their work to clients?

Marketing knowledge.

Explanation:

Marketing traditionally refers to all activities that a company performs to promote the sale of products or services. Traditionally, marketing has been seen as the totality of all activities aimed at promoting the exchange of products or services together with the sales department.  

Today, in most developed economies, consumer needs play a more important role than the presence of surplus supply. Marketing has thus become a pre-eminent discipline in which identifying needs has become central. Therefore, all professionals who want to maximize their sales should have knowledge of this discipline, in order to cover most of their clients' needs.