“like” needs an object for the comparison. Something can’t just “look like”, it has to look like something. “What” is an indirect reference to an object so you can say what it looks like.
“How” is a reference to an adjective or a description, so it doesn’t need another word to make it a comparison. How does the cave look? It looks terrifying.
Many native English speakers don’t know them. To them (myself included) it just doesn’t “sound right” but I couldn’t tell you why it’s wrong.
“like” needs an object for the comparison. Something can’t just “look like”, it has to look like something. “What” is an indirect reference to an object so you can say what it looks like.
“How” is a reference to an adjective or a description, so it doesn’t need another word to make it a comparison. How does the cave look? It looks terrifying.