Your first syntax errors are here:
Dim worksheetmaster As String = "Master"
Dim worksheettocheck As String = "New"
You can't do that. Instead, you would need to use:
Dim worksheetmaster As String
Dim worksheettocheck As String
worksheetmaster = "Master"
worksheettocheck = "New"
Even better would be to assign them to point diectly at the worksheets, but let's work with your code as much as possible instead of totally rewriting it.
For the countif, you cannot join ranges that way. You haven't even assigned a value to i, but assuming i = 1, your code:
softcount = Evaluate("=COUNTIF(Range('" & worksheettocheck & "'!A:A'" & worksheetmaster & "'!A" & i & ")"Soft")")
evaluates to total nonsense in VBA:
softcount = Evaluate(=COUNTIF(Range('New'!A:A'Master'!A1)Soft))
Now, from what I can tell, what you are trying to do is to count how many times the value in cell Master!A & i appears in the range New!A:A, depending whether Master!A & i="Soft" or Master!A & i="Hard". So let's see if we can find code that will do that.
For data we enter "Soft" into Master!A1 and "Hard" into Master!A2. Then we enter random "Soft" or "Hard" into various cells in the column New!A:A.
Now your code looks like this:
Dim worksheetmaster As String
Dim worksheettocheck As String
Dim softcount As Long, i As Long, hardcount As Long
worksheetmaster = "Master"
worksheettocheck = "New"
i = 1
softcount = Application.CountIf(Sheets(worksheettocheck).Range("A:A"), Sheets(worksheetmaster).Range("A" & i).Value)
i = 2
hardcount = Application.CountIf(Sheets(worksheettocheck).Range("A:A"), Sheets(worksheetmaster).Range("A" & i).Value)
This is inefficient and limited, but it retains as much of your original code as possible, and it works.
Edited to add: if "Hard" is in Master!B & i instead of A & i then the code becomes:
i = 1
softcount = Application.CountIf(Sheets(worksheettocheck).Range("A:A"), Sheets(worksheetmaster).Range("A" & i).Value)
hardcount = Application.CountIf(Sheets(worksheettocheck).Range("A:A"), Sheets(worksheetmaster).Range("B" & i).Value)
=countif('" & w1 & "'!A:A,"'" & w2 & "!A:A".....