you already have a function named activateThisColum() which is accepting 'choiceA', 'choiceB', 'choiceC', or 'choiceD'
So you just need to add the one line to that function to set the hidden field value:
$("#hidden_field").val(myvalue);
-Change #hidden_field to your field id (Keep the # as that means use the Id to match on hidden field id).
-Then change myvalue to match the variable parameter of your activateThisColumn() function.