If you need to create the list of unique part numbers, you can copy column A, paste it to column D, then go to the Data tab and click Remove Duplicates.
You can also use a Pivot table. Starting just with your A and B columns (nothing else yet), select those 2 columns, then on the Insert tab click Pivot Table, click OK. Now on the right side of the screen, drag Part # down to the Rows box. Drag Qty to the Values box. Now click where it says Count of Qty > Value Field Settings > Sum.
Excel has a lot of ways to do this. Hope this helps!
Well, how many part numbers do you have? If it's just a few, and you don't mind typing them out then you can use SUMIF:
Ex: (This range starts in A1 and ends in B21)
and using this to find the sum of all occurrences of "a":
If you are needing to find all unique part numbers, and then sum them, you can use this array formula:
Where I1 is the cell directly about where you want the new list of unique part numbers, so then I2 is the beginning of the list of unique part numbers. A1:A21 is the range of all your part numbers.
Make this new list, and then use the SUMIF formula next to each part number, but replace "a" with the corresponding part number next to it.