<form method="post" action="index.php">
<label>Выбирите ФИО</label>
  <select name="fio" onchange="fn()">     
    <?php 
   
    $fio = mysql_query("SELECT DISTINCT fio FROM price"); 
    
    while (($fioresult = mysql_fetch_array($fio)) !== false) 
    
    { 
    
      print_r ("<option value=\"$fioresult[fio]\"> $fioresult[fio]</option>"); 
    
    } 
    
    ?>
  </select>
  <input type="submit" name ="submit" value="Ok" />
</form>


<form method="post" action="index.php">
<label>Выбирите машину</label>
  <select name="carmodel" onchange="fn()">     
    <?php  
  
    $postfio = $_POST['fio']; 
    
    $carmodel = mysql_query("SELECT DISTINCT carmodel FROM price WHERE fio='$postfio'"); 
    
    while (($carmodelresult = mysql_fetch_array($carmodel)) !== false) 
    
    { 
    
      print_r ("<option value=\"$carmodelresult[carmodel]\"> $carmodelresult[carmodel]</option>"); 
    
    } 
      
    ?>
  </select>
  <input type="submit" name ="submit" value="Ok" />
</form>  


<form method="post" action="index.php">
<label>Выбирите дату</label>
  <select name="cardate" onchange="fn()">     
    <?php  
    
    $postfio = $_POST['fio'];
    
    $postcarmodel = $_POST['carmodel']; 
    
    $cardate = mysql_query("SELECT DISTINCT cardate FROM price WHERE fio='$postfio' AND carmodel='$postcarmodel'"); 
    
    while (($cardateresult = mysql_fetch_array($cardate)) !== false) 
    
    { 
    
      print_r ("<option value=\"$cardateresult[cardate]\"> $cardateresult[cardate]</option>"); 
    
    } 
      
    ?>
  </select>
  <input type="submit" name ="submit" value="Ok" />
</form>

<input type="hidden" name="fio" value="<?php $postfio = $_POST['fio']; echo $postfio; ?>">