It would appear you are trying to go into PHP mode while already in PHP mode, as you start with an "echo" command, then in the middle of the string have a "<?php . . . ?>" expression. Presumably what you want is something like:
echo '<td><input class="briefed" type="text" name="briefed" ';
if(isset($_POST['name'])) {
echo "value=\"{$_POST['name']}\"";
}
echo ' /></td>';