How old was Shem when he died?
Shem lived 600 years, from 2446 BC to 1846 BC.
Shem died at 600. The chart places his birth at 2446 BC and his death at 1846 BC, on the Ussher chronology it follows. Son of Noah; father of the Semitic peoples. (Gen. 11:10-11)
See it in context
A date means more beside its neighbours. The chart puts this answer in place next to everything happening around it — biblical and world history across the same six thousand years.
Now see where it sits
Everything on this page has a place on one 45×37″ chart — and once you can see what came before and after it, it stops being a fact and starts being a story you can follow.