In order to solve this problem, you will need to be aware of a number called "Avogadro's number." Avogadro's number, #6.022*10^23#, details the number of molecules/atoms in #1# mole of substance. Keeping this in mind, here is the dimensional analysis setup for this particular question (we are converting from moles #"S"_2"O"_3# to molecules of #"S"_2"O"_3# (using Avogadro's number) to number of atoms).
#0.67" mol" " S"_2"O"_3 *((6.022*10^23" molecules"" S"_2"O"_3)/(1" mole of ""S"_2"O"_3))*((5" atoms" )/(1" molecule ""S"_2"O"_3))=color(red)(2.0*10^24" atoms"#
Remember that I could have messed up the actual calculations, so I recommend that you type it into your calculator once again to check.
In case you were confused where I got the #5# from, #"S"_2"O"_3# has #2# #"S"# atoms and #3# #"O"# atoms. Since #2+3=5#, this tells us that one molecule of #"S"_2"O"_3# has #5# atoms.
I hope that helps!
