The Fed has already killed inflation. They and the market just don't realize it yet. Everyone is fixated on the year-over-year change, but that's not the right way to measure inflation in real time. There is significant lag in that data. We all know that prices were much lower last year than they are this year.
What is more important is looking at the monthly change in prices, not the annual. Are August 2022 prices higher or lower than July 2022, not August 2021, and by how much? That's what to measure and report on. See chart above comparing the year-over-year change to the one month change annualized.
You will see the one month change annualized is more lumpy to report on compared to the smoother year-over-year comparison. But what stands out is that inflation measured this way is already below the Fed's 2% target for two months running. This means the Fed has effectively accomplished its goals, and should approach any further interest rate increases with caution.
For the math geeks out there, here is how this one month change annualized statistic is calculated. It's easy to do in the data, but the trick is to change the monthly change into an annualized stat. You do this by assuming that the monthly change will continue for a full 12 months instead of just one month. The math is to take the monthly change in price levels and to compound it to the power of 12. Do not multiply it by 12 as that is not how price levels work. Example math for the month of Aug 2022 is below according to the Fed's data (source https://fred.stlouisfed.org/series/CPIAUCSL).
Aug 2022 price level = 295.620
July 2022 price level = 295.271
Aug/July = 1.00118
1 month % increase from Aug to July = 1.00118-1.0*100% = 0.118%
Annualized change = 1.00118^12-1.0*100 = 1.428%
Note this does not equal 0.118%*12 = 1.418%