You don't say how you want the match to be made.
If you want the dates to match exactly:
$query = "SELECT * " .
"FROM my_table " .
"WHERE `from` = '" . $from_date . "' AND `to` = '" . $to_date . "'";
or, if you want the selected range to be completely within the given range:
"WHERE `from` <= '" . $from_date . "' AND `to` >= '" . $to_date . "'";
or, if you want the any part of the selected range to be within the given range:
"WHERE (`from` <= '" . $to_date . "' AND `to` >= '" . $from_date . "') " .
"OR (`to` >= '" . $from_date . "' AND `from` <= '" . $to_date . "')";
Etc.