The key here is the fact that 1 mole of any element contains 6.022 * 10^(23) atoms of that element, as given by Avogaro's constant.
So if your sample contains 1 mole of iron, it contains 6.022 * 10^(23) atoms of iron. Similarly, if a sample contains 1 mole of potassium, it contains 6.022 * 10^(23) atoms of potassium.
Now, you know that iron has a molar mass of "55.845 g mol"^(-1). This means that every time your sample contains 1 mole of iron, it will have a mass of "55.845 g". This means that 6.022 * 10^(23) atoms of irion, the equivalent of 1 mole of iron, havea mass of "55.845 g".
Potassium has a molar mass of "39.0983 g mol"^(-1), which means that 1 mole of potassium has a mass "39.0983 g". This means that 6.022 * 10^(23) atoms of potassium have a mass of "39.0983 g".
So, use this to find the number of atoms of potassium present in "780 g" of potassium.
780 color(red)(cancel(color(black)("g"))) * (6.022 * 10^(23) quad "atoms K")/(39.0983 color(red)(cancel(color(black)("g")))) = 120.137 * 10^(23) quad "atoms K"
Now all you have to do is to figure out how many grams of iron will contain 120.137 * 10^(23) atoms of iron.
120.137 * color(blue)(cancel(color(black)(10^(23)))) color(red)(cancel(color(black)("atoms Fe"))) * "55.845 g"/(6.022 * color(blue)(cancel(color(black)(10^(23)))) color(red)(cancel(color(black)("atoms Fe")))) = color(darkgreen)(ul(color(black)("1100 g")))
The answer is rounded to two sig figs, the number of sig figs you have for the mass of iron.
Notice that because 1 mole of atoms of iron is heavier than 1 mole of atoms of potassium, which is essentially saying that 1 atom of iron is heavier than 1 atom of potassium, the mass of iron that contains the same number of atoms as the number of atoms of potassium present in "780 g" of potassium is > "780 g".
