¿Cómo que cómo?

This is an expression you'll want to be familar with. 

Don't try to come up with a literal translation, it just won't work.  This is something you'll have to memorize.

Let's look at a simple conversation to figure out what this means.

Esposa:  Amor,  ¿puedes lavar los trastes?
Esposo:  Bueno, pues, es que no sé como lavar los trastes.
Esposa:  ¿Cómo que no sabes lavar los trastes?

If you don't know, "trastes" are dishes.  And "lavar los trastes" is to wash the dishes.  So what does washing dishes have to do with today's phrase you ask?  Let's get back to our conversation to find out.

The key to this is the last sentence in our dialog:

¿Cómo que no sabes lavar los trastes?
What do you mean you don't know how to wash the dishes?

This is clearly an unexpected surprise to our beloved wife.  But she could have expressed her surprise a little differently:

¿Cómo que cómo?
What do you mean you don't know how?

¿Cómo que cómo? is just a shortened way to express surprise. 

Someone asks a question you just can't believe:

¡Cómo es posible que preguntes eso!

You can shorten that to...

¿Cómo que cómo?


You can use this same structure to ask:

¿Cómo que qué?
What do you mean "what"?

¿Cómo que dónde?
What do you mean "where"?

¿Cómo que cuándo?
What do you mean "when"

¿Cómo que para qué?
What do you mean "for what"?

That's it!  Pan comido right?

¡Hasta la próxima!