Read your code top to bottom.....
Firstly you connect to the database etc.
Then,
$sql = "INSERT INTO employees (First_Name, Last_Name, How_Many, Children) VALUES
('$First_Name','$Last_Name','$How_many','$Children
')";
This creates a variable called $sql with your INSERT statement.
Then you come out of PHP with ?> and into normal HTML to create your form.
Your form has ACTION=done.php which says when you click on the submit button to send the form data to done.php.
There's nothing in your script which actually performs the INSERT you created in $sql.
I suggest you take all your PHP code out of this page and leave it as a plain HTML form. Then in done.php you can do the INSER processing.
# File done.php
# Retrieve the POSTed form values
$firstname = $_POST['First_Name'];
$lastname = $_POST['Last_Name'];
$howmany = $_POST['How_Many'];
$children = $_POST['Children'];
# Connec to the database
$db = mysql_connect("localhost", "root", "my_password");
$link = mysql_select_db("mydb",$db);
# Create the SQL to do the insert
$sql = "INSERT INTO employees (First_Name, Last_Name, How_Many, Children) VALUES
(\"$firstname\", \"$lastname\", \"$howmany\", \"$children\")";
# Then run it
$result = mysql_query($sql, $link);
# Then check the result
if ($result != '0') {
echo "You have inserted a record for : " . $firstname;}
else {
echo "Insert has failed";
echo "<BR>SQL STATEMENT:<BR>";
echo $sql;
Give that a bash!