I am trying to order a new turbo for my 2006 F-350 6.0 diesel. It asks for the engine number or the OEM Turbo part number. Where do I find these?

 

Check here for engine number location http://www.backglass.org/duncan/ps60...l/ps60_008.jpg. Turbo sticker is kind of obvious right on the turbo if it's still there.

 

Not sure where you're ordering from, but here's a new '06 turbo with no core:
Garrett 743250-5025S GT3782VA Stock Replacement Turbocharger

There's a discount code somewhere for FTE members to get a % off, you can search threads for it or try to find Xtreme as a vendor on here and it might be in the guy's sig line.