We have to determine the order of 7 objects, 2 pieces of china - M P, 2 pieces of glassware - W J and three utensils - K F S. The rules tell us that a knife is washed before the spoon and all objects of the same type are washed together, so the possible order for the utensils are either K S F or K F S or F K S - which allows us to conclude that knife must come either 1st or 2d among utensils. The rules also tell us that glassware is washed either after utensils or after china but not after both, meaning two pieces of glassware have to be in the middle, resulting in two possible order options:
U U U G G C C C C G G U U U
Since we know that the knife can not be #3 among the utensils washed in either of these scenarios (a spoon must always come after the knife), we can conclude that the knife can neither be #3 in the overall order in the fist scenario nor #7 in the second scenario.
Let me know if this makes sense and if you have any other questions.
