"How it looks like"

My German English professor regularly uses the phrase "how it looks like", for example in questions.

How does the social media market look like today?

In my head, it always sounds wrong – I'd rather use "what it looks like" or "how it looks".

What does the social media market look like today?

How does the social media market look today?

Which of the three usages are correct?

An interrogative phrase How replaces the preposition phrase including any prepositions:

• How [does it look like something]?

An interrogative phrase with What just replaces a noun phrase:

• What [does it look like something]?

So, in short, the Original Poster's intuitions are correct. If we try to use How but not delete the preposition, the sentence will be ungrammatical:

• *How does it look like? (ungrammatical - like should be deleted)