Merging Columns of Data

HELP!

I have seen the concatenate function, but not sure if it would apply here...

I have a list of accounts and serial numbers and two date columns that I would like to combine and sort.

Column G = Warranty End Date
Column H = Support End Date

I would like both of these columns combined for one master list of dates available to sort in ascending order with corresponding account and serial number data. HOWEVER, some accounts have dates listed in BOTH of the columns - in which case I'd like column H to take precedence.

Any help would be greatly appreciated! I'm STUCK!
Ruby