can someone explain to me how double washing works?

When you add level up AP to MP it takes your INT into account. So you'll gain 1 more MP for every 10 INT you have just like when you level up.

You wear INT equips, level up, add your AP into MP, then reset out of MP and add to HP to be washed out again.

http://forums.asiasoftsea.net/showthread.php?t=104264