Earlier quoted context omitted.
You should say more about why you think 6-8% unemployment is required. From September 2014 - February 2020, unemployment was below 6% without signs of significant inflationary pressure. I'm not saying you're wrong (those periods are different from the present in a lot of ways), just that your reasoning isn't very apparent.
I didn't say that inflation would reappear at 5.99% unemployment. They need >6% so there's a gap between here and there. Right now we're clearly at the rail and unemployment has not budged. The jobs overhang has significantly abated, but that has been a short-term reaction to the policy changes, and it can change back on just as short of a term.
I didn't say you did, just that you haven't said anything to motivate the 6-8% number. It's plausible sounding, but as far as what you've said so far, you might as well have drawn those numbers out of a hat.