You have to concatenate the value of the combo box to the string, otherwise you are looking for the string "[Forms]![frmTasks]![cmbProject]"
This might get you moving again:
(Assumes the combo box is text)
Code:
Dim dbsCurrent As DAO.Database
Dim rsCount As DAO.Recordset
Dim result As String
Dim sSQL As String
Set dbsCurrent = CurrentDb
sSQL = "SELECT Tasks.Resource_F, Tasks.Resource_L, Tasks.Project_Lead, Tasks.Resource_ACF2ID"
sSQL = sSQL & " FROM Tasks"
sSQL = sSQL & " WHERE Tasks.Project_Name = '" & [Forms]![frmTasks]![cmbProject] & "' AND Tasks.Project_Lead =True"
Set rsCount = dbsCurrent.OpenRecordset(sSQL)
result = rsCount![Resource_F]
' result1 = rsCount![Resource_L]
rsCount.Close
Set rsCount = Nothing
Set dbsCurrent = Nothing
If result > 0 Then
MsgBox "There is already someone checked:" & result & " " & result1, vbInformation, "Example"
Me!chkLead = False
End If
edit: I see June beat me again