OK, if that's the same fragment, that means that both the EcoRI cut sites are between position 4200 and 10,700, right?, since those are the two HindIII sites that cut out the 6200 bp piece. Well, now; let's take a look at PstI + EcoRI: what do we have that's longer than 4200 bp (since we have decided that there is no Eco site between positions 10,700 and 4200)? Hey - there's only one: 5400 bp! Boy, that's convenient! So, since the PstI site is at position 0, that means that the EcoRI site has to be at position 5400. Now let's check - if that site is at 5400, what do we get when we cut with HindIII and EcoRI - cuts at 10,700, 4200 and 5400, giving us 6200 and 1200 bp fragments. What do you know! I think we're on the right track, because that's two of the four pieces given.
Now we have to work out where that other cut site goes. We know it's going to be between positions 5400 and 10,700 and 1800 bp from one or the other. That means either position 7300 or position 8900. Do you see how it has to be like that? The 1.8 kb piece from the Eco + Hind double-cut? So, let's see what we get if we put it at position 7300.
Now we have, starting from the beginning, PstI - 0; HindIII - 4200; EcoRI - 5400; PstI - 5900; EcoRI - 7300; HindIII - 10,700. Each enzyme cuts twice, and we already know that the HindIII and PstI sites work. So, what about the EcoRI sites - if we have one at 5400 and one at 7300, that gives us EcoRI fragments of 10,800 and 1900 bp. Darn, that doesn't look right. Well, let's try our other option, of putting the EcoRI site at 8900 instead of 7300. Now what do we get if we cut with EcoRI? Yo! 3500 and 9200 bp! So, cut with HindIII and EcoRI again to check - cuts are at 4200, 5400, 8900 and 10,700. That gives us 6200, 1200, 3500 and 1800 bp pieces. I think we've got it!
Now go back over this and work it through from the beginning until you understand how you put the pieces together so that the result works out. It seems tricky, but it's actually pretty simple; it's just a big pain in the neck going through the steps and checking what you get if you have a cut site in a particular position.
Now, you mustn't forget that the numbers I used for the positions are only for relative location - the plasmid could be flipped over, in which case the positions of the sites would be PstI - 0, HindIII - 2000, EcoRI - 3800, PstI - 6800, EcoRI - 7300, HindIII - 8500. Not to mention that I just arbitrarily chose to put the PstI site at position 0; who knows what the real location is? All we care about is where the cut sites are located relative to each other.
I hope this helps a bit; I enjoy puzzles like this but I know not everybody does...