The error comes from a syntax error in your formula. So Excel (not VBA) complains about that error by raising an "application-defined" error to VBA, and VBA shows it to you. You simply cannot enter an invalid formula into a cell. If you try manually from Excel, you will get something like "There is an error with that formula".
Now, while it's hard to write a complicated formula in Excel, it's even harder to get it right from VBA. Following things can help to find the problem:
(1) Don't write the formula direct into the excel range. Use an intermediate variable:
Dim formula as string
formula = "=IFERROR(VLOOKUP(LEFT(RC[-28],8),'" & x & "]SheetName'!C1:C3,3,0,)""Not Available"")"
Debug.Print formula
Sheets("T0").Range("AC2").FormulaR1C1 = formula
(2) Write the formula into Excel manually, keep the cell active, switch to the VBA environment and type in the immediate window:
? activecell.FormulaR1C1
Compare the result with the content of the formula-variable. If they are not identically, you probably have found your problem.
In your case, you have a misaligned comma in the formula. Look at C1:C3,3,0,) - it should have the closing parenthesis before the comma: C1:C3,3,0),
"=IFERROR(VLOOKUP(LEFT(RC[-28],8),'" & x & "]SheetName'!C1:C3,3,0),""Not Available"")"
I cannot guarantee that this the only error in the formula - but I hope it can help to narrow down such problems.
Debug.Print xto see that value as you test. Also try assigning a simple value like3to the sheet formula. We can't tell if that sheet reference is valid.