Learn Farsi: او این انتقاد را پسندید.

The present stem of the verb پسندیدن (to like/approve) is پسند. This stem is highly productive for creating compound adjectives that describe a characteristic trait. By adding a noun or adjective in front of it, you get common words like مشکل‌پسند (picky / hard to please, literally "difficulty-liking") or هنرپسند (art-loving).

In English, we say "approved of". Why isn't there a preposition like از in the Farsi sentence?

Unlike the English phrase "approve of," the Farsi verb پسندیدن is a direct transitive verb. It takes a direct object without needing a preposition. Since the object here is specific (این انتقاد - this criticism), it must be followed by the definite object marker را.

Could I use دوست داشت instead of پسندید to mean "he liked this criticism"?

You could, but پسندید is much better suited here. While دوست داشتن is a broad "to like" or "to love," پسندیدن implies evaluating something and finding it acceptable, favorable, or to your taste. That is why it translates so well to "approved of" in an evaluative context like receiving criticism.

Are there other common words related to انتقاد (criticism) that I should know at this level?

Yes. انتقاد is an Arabic loanword, and its root is used in several related terms you will encounter at the B2 level. A very common one is (critic / reviewer). You will also frequently see it used as the compound verb (to criticize).