How to rationalise the protonation of a compound with multiple double bonds?
The key is delocalization of the positive charge in carbocations.


Most stable carbocation that you can get from the protonation of the compound above. Reasons for it being the most stable:


The carbocation is a hybrid of the two resonance forms (below) – the π bond is delocalized over three C atoms and the positive charge is delocalized over the two C’s (the ones with + charge)
In one of the resonance forms, the positive charge is at a tertiary carbon atom



Second most stable carbocation.


The carbocation is a hybrid of the two resonance forms (below) – the π bond is delocalized over three C atoms and the positive charge is delocalized over the two C’s (the ones with + charge)



When protonation happens on the third pi bond. No delocalization - not as stable as the carbocations shown above.


There are other possible ways in which the compound could have been protonated (below), however none of them are as stable as (1) or (2), because there is no delocalization.