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Using your data, it seems to work fine here. Even using the structured reference. Note that with the formula in the same row, you may only need to refer to the column header. And with the formula within the table, you can use an unqualified (no table name) reference.
Note the formula in the formula bar, next to fx.
As to why you are seeing a formula and not a result, be certain the cell was formatted as General BEFORE you enter the formula. If that is not the problem, I would have to examine the workbook.
Actually, the formula in Column F, as written, will return an ARRAY of all the values in the Asset BarCode column. You are only seeing the one that is on the same row since it displays the first, and there is only one row in your sample table. To "force" the formula to return ONLY the one value, and not an array, you need to add the ThisRow parameter, so the formula might look like:
=RIGHT(Table1[[#This Row],[Asset Bar Code]],7)