How do I display a MySQL error in PHP for a long query that depends on the user input?

Use this:

mysqli_query($this->db_link, $query) or die(mysqli_error($this->db_link)); 
# mysqli_query($link,$query) returns 0 if there's an error.
# mysqli_error($link) returns a string with the last error message

You can also use this to print the error code.

echo mysqli_errno($this->db_link);

Take a look here and here

I use the following to turn all error reporting on for MySQLi

mysqli_report(MYSQLI_REPORT_ERROR | MYSQLI_REPORT_STRICT);

*NOTE: don't use this in a production environment.

Use function die():

or die(mysql_error());