Find data from a table using 4 inputs

Will a "Check "value only appear once in Input i.e. in only ONE of the 6 columns? Your posted file only has a single occurrence of each.

One way...With a helper column...

Sub J3v16()
Dim Chk, sNum As String
sNum = Range("B2") & Range("C2") & Range("D2") & Range("E2")
With Sheets("Inputs")
    .Range("H2:H" & .Cells(.Rows.Count, 1).End(xlUp).Row).Formula = "=CONCATENATE(A2,B2,C2,D2,E2,F2)"
    Chk = Application.Match(sNum, .Columns(8), 0)
    If Not IsError(Chk) Then
        Sheets("Check").Range("G2") = .Range("G" & Chk)
    Else
        MsgBox "This selection of numbers has not been entered yet", vbInformation, ""
    End If
    .Columns(8).ClearContents
End With
End Sub

@Sintek: Fallen at the first hurdle!

This only works if the "Check" values (helper column) are in the same sequence as the Input column data

Input: 609C/2967A/44E/3012A vs "Check": 609C/44E/3012A/2967A for match on row 47.

Sub find4()
Dim ar, ip, check
Dim ws1 As Worksheet, ws2 As Worksheet
Set ws1 = Worksheets("Inputs")
Set ws2 = Worksheets("Check")

Application.ScreenUpdating = False

ws1.Activate
With ws1                                            ' Store Input data in array
ar = .[A1].CurrentRegion
nr = .Cells(Rows.Count, 7).End(xlUp).Row - 1        ' Count of rows of data
End With

ws2.Activate

With ws2
    check = .Range("B2:E2")                         ' Get "Check" parameters
   .[G2]=""
End With

ReDim ip(1 To nr)                                   ' Dimension match array

For k = 1 To 6                                      ' Loop trough Input columns

    For j = 1 To nr                                 ' Create match data for column "IPk"
     ip(j) = ar(j + 1, k)
    Next j
    
    n = 0
    For i = 1 To 4                                    ' Loop through "Check" parameters to find a match
        r = Application.Match(check(1, i), ip, 0)
        If Not IsError(r) Then                        ' A match found in this column
            For l = 1 To 4                            ' Check if all "Check" paramters are in this row
               For m = 1 To 6                         ' loop through columns for row "r"
                   If check(1, l) = ar(r + 1, m) Then ' "Check" found
                       n = n + 1                      ' Count of matched "Check" parameters
                       Exit For
                   End If
               Next m
            Next l
            If n = 4 Then                           ' All Found in this row
               ws2.Range("g2") = ar(r + 1, 7)         ' Output "Best Number"
               Exit Sub
            End If
        End If
    Next i
        
Next k

MsgBox "This selection of numbers has not been entered yet"


Application.ScreenUpdating = True

End Sub

@ John...Got confused at your response until I only NOW noticed this...

where those four numbers are together, in any order, across the row

Oops...My bad...Yep, fallen hard lol...

@ Sintek: equally my offering will fail if a "check" value occurs more than once in a given column (as I use MATCH).

Pick yourself up, dust yourself down and off you go!!!

Pick yourself up, dust yourself down and off you go!!!

True...I will revisit this a bit later...
For you...Just a heads up...6 + variables not declared...
Add Option Explicit to top of your code and run...

Please try

Private Sub CommandButton1_Click()
Dim rs, l&, d$
l = Sheets("inputs").Cells(Rows.Count, 7).End(xlUp).Row
d = "=Inputs!A2:F" & l
rs = Evaluate("INDEX(Inputs!G2:G" & l & ",MATCH(4,MMULT((B2" & d & ")+(C2" & d & ")+(D2" & d & ")+(E2" & d & "),{1;1;1;1;1;1}),))")
    If IsError(rs) Then
        MsgBox "This selection of numbers has not been entered yet"
    Else
        [g2] = rs
    End If
End Sub