Yes, it is safe to plug a 6 amp washing machine into a 16 amp switch or socket. The current rating of the switch or socket (in this case, 16 amps) represents the maximum amount of current it can safely handle. As long as the appliance (in this case, the LG 6.5kg washing machine) has a current draw below or equal to the switch or socket's maximum rating, there should be no issues with safety.
In this situation, the washing machine has a current draw of 6 amps, which is well within the capacity of the 16 amp switch. The switch is designed to provide an additional safety margin, allowing it to handle more current than what the washing machine requires, which is perfectly fine.
Just make sure that the plug and socket connections are secure and that the wiring is in good condition to avoid any electrical hazards. If you have any doubts or concerns about the electrical setup, it's always a good idea to consult a qualified electrician to ensure everything is safe and up to code.