how many wings does a cockroach have?

Answer 1

They usually have 4 wings, but the pair of forewings has a leathery texture (those are the ones one sees when the cockroach is not flying), while the hindwings are fanlike and usually protected under the forewings.

However, there are also cockroach forms with underdeveloped or absent wings, even within the same species (these are called micropterous and apterous forms, respectively).
The latter are those cockroaches in which you can see the segmented abdomen (not covered by the leathery wings).

Answer 2

According to this site, a cockroach quiz, they have four wings.
http://www.elton.iinet.net.au/page118.html