From your post i assume that you do not want to deal with server side programming but i will mention it briefly. If you submitted the user selection from the request you could get the value of his selection and use it on the backend. So, in a servlet or portlet for example your could do
String state =request.getParameter("idOfSelectBox");
<select id="state" name="state">
<option value="newyork">New York
you then need to notify your page that the value has changed so your selectbox tag now looks like this:
<select id="state" name="state" onchange="storeState()">
you now need to write the actual code of storing. You need a variable to store the information in and a simple function to store it
this create a variable and then gets the value set in you selectbox identified by the id you gave it and stores it.
to test that you now have stored the information you can put a button that creates an alert showing the information
<button onclick="showState()">Click Me</button>
alert('Your selection was:'+state);
this puts an onclick event that triggers the function showState(). This function gets the value stored previously in the variable state and presents it in an alert.
I hope I helped
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