US Second inflation wave is coming? Questionable policy change for the fed to decide

There's a possibility that we might witness US inflation to increase once again. The reason for this is due to inflation rate chart is going sideways for last 3 month. This is very concerning because FED is in a tricky situation.

The easy narrative is that the rates policy couldn't tame inflation which could cause delayed rates or even rate increases again in the future if inflation is proven to be stubborn and rises again.

These chart are similar on the 1980 recession when FED made a policy error which stagnate economic growth. We already see the delay from March to June this year and if the PCE and CPI on March data coming in hot on April news. Then these hypothesis could be proven true.