For the sake of simplicity we'll start with EcoRI and as it only cuts once we'll say that it cuts at position 0kb.
Eco + Bam obviously only cuts twice so if Eco cuts at 0 then Bam must cut 1.9kb away (at position 1.9kb)
PstI cuts 1.5kb away from BamHI: this can either be at point 0.4kb (BamHI's1.9kb minus 1.5kb) or at 3.4kb (1.9+1.5). ---> But as PstI/EcoRIgives a 3.4kb frag this means PstI's site is at 3.4kb.
SstI/Eco gives a 0.8kb fragment but as this is missing for the Bam/Sst digest you can assume that BAm must cut in the middle of it, thus there are Sst sites 0.3 and 0.5kb away from the Bam site: either at 1.4/2.2 or 1.6/2.4. As the Eco/Sst digest gave a 1.4kb fragment we can assume it is the former option. (IE SstI cuts at 1.4kb and 2.2kb.)
In some ways we can ignore the last two digests that we have data for as the other two fragments from the Eco/Sst digest are equal in size so must be (negative) 1.9 and 3.8kb away from EcoRI. This gives us cut site of 4.1kb and 2.2kb (The second one we already know!)
Could someone have a look at the picture of the SDS-PA gel below? It shows the gel after recombinant protein samples were electrophoresed then blotted onto a PVDF membrane for a Western. The gel was then Coomassie stained/destained. We would normally expect just the one ~42kDa band (possibally with a few contaminant bands) in the middle of the gel, which is there, but there is a strange speckling throughout the entire gel.
The Western Blot result is also shown and makes no sense either (but that's most likely a separate issue).