In Washington we pay a sale tax of 8.3%
In Oregon there's no sale tax.
People who come to shop from Oregon to Washington don't pay tax because they live in Oregon.
Does that mean that if I go buy something to Oregon I have to pay tax because I'm from Washington.

If I do have to pay taxes; What if I pay with debit card? Will They know that I'm from Washington and will they charge me sale tax or not?

Should I just take cash instead?
That way They wont know that I'm from Washington.