Rearrange the parts of the sentence in the correct order.
We should learn our lesson
P-from this history and stay away
Q-of our neighbours
R-from interfering in the messy domestic politics

Let's logical connect the fragments:
The introductory segment is "We should learn our lesson". This is naturally followed by the prepositional phrase explaining where to learn the lesson from: P ("from this history and stay away").

The phrase "stay away" is typically followed by the preposition "from". This connects perfectly to part R ("from interfering in the messy domestic politics").

"The messy domestic politics" must belong to someone, which connects it to part Q ("of our neighbours").

Thus, the correct sequence is PRQ.