The PCC first makes the primary alcohol turn into an aldehyde.
Then, the methanol and H+ turn the aldehyde into a hemi-acetal.
We have KMnO4, but it doesn't say it's hot or concentrated, or both, so we assume it doesn't cleave anything. What we assume it does is open up the alkene into the diol like you see there at the end, adds syn by the way.
Now, the final part, H3O+, reverts the hemi-acetal to the aldehyde. You should remember that H3O+ always reverts these ketals and acetals (hemi as well).
Hope that helps.