You can create MySQL database with create database DATABASE_NAME command.

root@host [~]# mysql
Welcome to the MySQL monitor. Commands end with ; or g.
Your MySQL connection id is 937316 to server version: 4.0.25-standard

Type ‘help;’ or ‘h’ for help. Type ‘c’ to clear the buffer.

mysql> create database bizhat;
Query OK, 1 row affected (0.01 sec)

mysql>

To delete a MySQL Database, use drop database command.

mysql> drop database bizhat;
Query OK, 0 rows affected (0.00 sec)

mysql>