My washing machine has this ending (it's inlet hose for water). What is the correct counter part that it should be connected to? I'm really confused by these screws.

It is a quick connect - the part with screws attaches to the tap nozzle using the screws and the white plastic slips over it and can be easily removed.  Make sure tight to nozzle when screwed fully in.

There are 3 parts. The metal one is fastened on the valve.

Yes. it's a 'universal' tap attachment and it's not really that quick.

 

Also note that when it comes to appliances and plumbing, Thailand sometimes isn't in the same universe.

Unless you want to use the "connect-disconnect" function on a tap, just cut that end off and use a standard faucet or hose connector with hose clamps.

Thanks!

Make sure it's earthed electric wise.