Summing column values if 2 criteria are met

[spoonpilot]

I am trying to find a formula to add the contents of cells in a column of a table, only if and when both of 2 criteria are met.

On Sheet A where the formula will be, I have 2 columns of dates - columns AF (month start) & AG (month end). For example, let's use range AF10:AG10

On Sheet B I have a rows of information in a table (B6:AN10000)

I want to find a sum total of the values in column X on sheet B (X6:X10000) in rows where the given date (in column Z (Z6:Z10000)) falls between the values in AF10:AG10 in sheet A, AND also where column C (C6:C10000) contains a numerical value of 5,6,7 or 8.

I was trying to do it using SUMIFS but am getting myself confused! You may also be confused by the way I've written the question, but I will happily try to clarify or give additional information if needed.

Any guidance would be greatly appreciated, thank you.

[wk9128]

Could you pls post a small example of your excel file ?
Provide a scenario showing exactly wheat you'd expect.