Pretty simple...a copy / paste from another article below. As noted, the Ducks would lose the tiebreaker to Arizona.

I will say, with all due respect to Arizona's more than exceeded expectations season, anything other than a UW vs UO rematch will feel like a major letdown not only for Oregon but the Pac-12 in general. Plus IF Arizona were to beat the UW(they only lost by a TD in the regular season) = no Pac-12 team in the Playoffs.

Here is the copy / paste...

"For Oregon to make it to the Pac-12 Championship game, there are two paths.

One is for the Ducks to beat Oregon State in their annual rivalry game next Friday. That would leave Oregon as the lone one-loss team in the conference behind Washington. Last year, the Beavers upset the Ducks 38-34.

The Ducks can also clinch if Arizona falls to Arizona State.

Arizona needs two things to happen: A win over ASU and an Oregon loss to Oregon State.

If the Wildcats win and the Ducks lose, both teams would have two Pac-12 losses and the Wildcats would edge the Ducks due to a tiebreaker. In this scenario, since Arizona and Oregon didn’t play each other this year for a head-to-head tiebreaker, the next tiebreaker is the two schools’ top common opponent. That would be Washington, which beat both Arizona and Oregon in October.

After that, though, the two teams’ next-highest common opponent is Oregon State. The Wildcats beat the Beavers a few weeks ago while in this scenario, the Ducks did not."

Go Ducks!