please solve and explain
how many gumballs in 1 mole can cover the earths surface in one year
It is a bit confusing what you are asking for. If you could type in the exact question that would be helpful. Then you would just need to work backward from the "units" of that answer. So suppose if they asked percentage of the earths surface in meters^2.
1 mole * 6.02x10^23 gumballs/per mole = (moles cancel and you get) 6.02x10^23 gumballs
6.022 x10^23 gumball x 0.001m^2/Gumballs (size of 1 gumball)= (gumballs cancel and you get) 6.02x10^20 m2
then you just put:
6.02x10^20 m^2 of gumballs/ suface area of the earth in m^2= (m^2 cancels and you get) a unitless number (which is what a fraction is) you then multiply by 100 to get a %.
Could you clarify your question a little? I can kinda see what you're asking, but the way it's worded is confusing. It looks like you're asking how much of the Earth's surface would be covered by a mole of gumballs (or what volume they'd take up, and what height/depth they'd be), but I'm not sure what the one year has to do with that.
In any case, it looks similar to this, except with gumballs instead of moles (it's a fun read): http://what-if.xkcd.com/4/