Aashish682 says:
var row = $(this).closest('tr');
var ID = row.find("td:first").text();
$("#<%=TextBox12.ClientID%>").val(ID);
You can't find directly the dropdownlist selected you in above manner just refer below code in below code you are finding the dropdownlist selected item value or text.
var row = $(this).closest('tr');
var ID = row.find("[id*=your dropdownlist id] option:selected").text(); // for selected item text.
$("#<%=TextBox12.ClientID%>").val(ID);
var row = $(this).closest('tr');
var ID = row.find("[id*=your dropdownlist id] option:selected").val(); // for selected item value.
$("#<%=TextBox12.ClientID%>").val(ID);