Can I correct my underbite with tooth extraction and braces? (photos)

I have been told my underbite is severe and that surgery is the only way to properly correct my underbite. However I have come across an orthodontist that identied that I have 12 upper teeth and 14 lower and his recommendation is to remove 2 of my lower bicuspids and then using braces to pull everything back in order to camouflage my underbite.