My coworker told me that he had a conflict with another one of my coworker and I wanted know exactly what happened between them so I asked:
"tell me what the exchange was like"
But I am not sure I should have said
"tell me how the exchange was like"
I guess one of the two is wrong (for the context I provided) but can someone point out the differences between them?
You should not use "like" for the second sentence, so it should be
tell me what it was like
tell me how it was
The first one is more natural, especially since you want to describe the quarrel that occurred during the exchange. If you say "tell me how it was", you are asking whether it was good or bad, if you say "tell me what it was like", you are asking what happened, the "experience" during the exchange and the outcome.
If you ask,
What was the exchange like?
then it is the same as "tell me what it was like", asking about the "experience" and what happened during the exchange.
Let's look at the first sentence:
Tell me what the exchange was like.
The nominal clause ("what the exchange was like") functions as the direct object of the verb "tell". It contains a subject ("the exchange"), a simple predicate ("was"), and a prepositional phrase ("like what", with the preposition postponed, which is often allowed in subordinate clauses). Everything makes sense, and this sentence is grammatical.
Now let's look at the second sentence:
Tell me how the exchange was like.
The preposition "like" no longer has an object (complement)! "How" is either an adverb or conjunction (depending on your interpretation), but neither of those parts of speech typically functions as an object. Because prepositions normally require objects, this sentence is incorrect. We could fix it simply by omitting the preposition:
Tell me how the exchange was.
This is now grammatical, but for the meaning that you intend, the original sentence ("tell me what the exchange was like") is probably better, as KB has noted in a comment.
Tell me what the exchange was like.
is asking for the respondent's impressions. Was it nasty or civil?
If you want to know about the outcome and what led to that outcome you might say
Tell me how the exchange went.
although either of these requests would be likely to produce the same response.
As others have noted,
Tell me how the exchange was like.
is wrong.
