Learn German: Die einfühlsame Klientin versteht die Abneigung doch sehr gut. - The empathetic female client actually understands the aversion very well.

Grammatically yes, but it sounds slightly odd. The structure wissen zu plus an infinitive usually implies having the skill or ability to do something (like knowing how to do something). Because understanding an emotion isn't really an active, practiced skill, using the plain verb versteht is much more natural here.

Why is doch translated as "actually" here instead of "but" or "yes"?

In this sentence, doch is used as a modal particle rather than a conjunction or an answer to a negative question. It adds the flavor of "contrary to what you might expect." It implies that someone assumed the client would not understand the aversion, but she actually does.

How is the adjective einfühlsame formed?

It comes from the reflexive verb sich einfühlen, which means to empathize or put oneself in someone else's shoes. Adding the suffix -sam turns it into an adjective describing someone who has that trait. The -e at the end is the standard adjective ending for a feminine, singular, nominative noun following a definite article.

What is the literal meaning of Abneigung?

It comes from the verb neigen (to lean or incline) and the prefix ab- (away). So it literally means a "leaning away" from something, which perfectly captures the English translations of "aversion" or "dislike."