What do you like?

I like cartoons.

How do you like? (Can we use this expressions as a complete question?)

I think we can use the following question.

ex) How do you like the shiny car?

Thank you for using the Jiskha Homework Help Forum again.

How do you like? = no; this is not complete. You need an object, such as "H ow do you like IT?" or as you wrote " How do you like the shiny car?"

Sra