If the time is 645am in Sydney what time is it in seattle?

It depends on the time of year.

If the U.S. is on Daylight Saving Time and Australia is not (1st Sun. of Apr. to 1st Sun. of Oct.), it's 1:45 PM PDT.

If Australia is on Daylight Saving Time and the U.S. is not (1st Sun. of Nov. to 2nd Sun. of Mar.), it's 11:45 AM PST.

During the other parts of the year, when both countries are on Daylight Saving Time, it's 12:45 PM PDT.