Feldman thinks that the no-false premise solution to the Gettier problem fails. Remember, the no-false premise solution (NFPS) to the Gettier problem is to say that the real problem with the Gettier cases is that people are forming justified and true beliefs based on false beliefs. Someone who believes the NFPS will think that we can avoid the Gettier problem if we avoid forming beliefs on false evidence or false premises. Feldman thinks that the NFPS does not solve the Gettier problem. He gives us cases where someone has a justified and true belief that is based on all true premises yet is still not knowledge.
In the original Smith and Jones case, Smith forms his justified, true belief "The man who gets the job has ten coins in his pocket." because he believes a false premise, "Jones gets the job."
In a Feldman-style version of this case, Smith would have the same justified and true belief "The man who gets the job has ten coins in his pocket." even if he believed this based on all true premises:
1. My boss said "Jones has ten coins and he will get the job".
2. My boss is usually right and he is also really honest about this kind of stuff.
Both premises are true. Smith has the same justified, true belief. Still, this is not a case where Smith actually has knowledge. Feldman attempts to show that the no-false premise solution is not restrictive enough because it does not exclude the possibility of all Gettier cases.