I'm a little confused on the dimensions: 2"x4'x8' sounds like pink foam or another insulating styrofoam. Styrene is a non-porous plastic material, usually used for building model structures and cars. I think it would cost a fortune for a 4'X8' sheet.
If it is styrene that you're asking about, then I would follow santafewillie's advice or head to your LHS to get one of the specific cements made for styrene. If it's foam, then you will want to use a contact cement intended for use with extruded foam. A hardware shop should be able to help you; Liquid Nails is a product that I have heard mentioned frequently for this use, but I can't remember the specific line. Regular carpenters glue isn't a great product for this application as the insulating properties of the foam inhibit the air ciruclation required to dry. Also, you should not use any solvent based product on the foam (including certain kinds of cement and spray paint) as it will eat away at the foam and potential release harmful fumes.
Hope I haven't muddied the waters too much, but I just wasn't sure it was styrene that you were asking about.