Pick a Pair of Packets

My friend Jeff likes his coffee sweet, so I wasn't surprised when I met him at the cafeteria, and on the table in front of him was a line of six packets of sweetener in a row, three pink followed by three blue:

        P P P B B B
      

As we were talking, my eyes rested on his fingers, which were idly shuffling the packets around the table in pairs. After a while, I noticed that he had rearranged the packets so that they alternated:

        P B P B P B
      

I thought nothing of it. But that night, I couldn't sleep, and I tried to relax by recalling how the packets had been shifted. All I could remember was that:

• Jeff made a total of three moves;
• Each move consisted of moving two packets, which were "neighbors", as a unit, to a new position in the line.

I give up, show me the solution.

This puzzle is sometimes known as Tait's counter puzzle after the British mathematician Peter Guthrie Tait, who described it in 1884.