<select>
в котором несколько <option value>.
$sql = "SELECT * FROM `brands` WHERE `district` = :district";
$params = [];
$sql = "SELECT * FROM `brands` ";
if (!empty($_GET['district'])) {
$sql .= "WHERE `district` = ?";
$params[] = $_GET['district'];
}
$stmt = $pdo->prepare($sql);
$stmt->execute($params);