If Stan bought 4 times as much of everything and paid 4 times as much:
cost of 12 kg potatoes and 8 kg apples = 4 * 39.10
Similarly, if Fia bought 3 times as much of everything:
cost of 12 kg potatoes and 21 kg apples = 3 * 94.60
Now you have two equations both of which have 12 kg potatoes in them. You can subtract all terms of the first equation from the terms of the second equation. Then solve for price of apples.
To be more formal, we might use a letter like P to stand for price of potatoes per kg and A to stand for price of apples per kg. Then on each side we have units are SEK.
12 * P + 8 * A = SEK 156.40
12 * P + 21 * A = SEK 283.80