In attached workbook I added 2 sheets for possible solution.
On sheet Budget are 2 separate Tables. One for original budget info, and another for later adjustments. To get what you want, you simply set autofilter for AdjustmentMonth field in adjustments Table e.g. to 2018 February.
On sheet SetUp you can select year. In another Table on SetUp sheet 1st of 12 months in selected year are calculated. This Table is a base for Data Validation List to select months in AdjustmentMonth field in Adjustments table (i.e. real entries in this field are dates like 1st of January 2018).
I couldn't place amounts in Adjusted Budget part in table on Sheet1 (your original table), so I left them out.
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