I found this answer by trial and error but later on worked it out with algebra.
This is what I first got by cancelling down:
GOLD SILVER BRONZE
France 7 2x 18
Italy x 25-2x x+2
Japan x+1 22-2x 18-x
Then I guessed that if it says at least 6 medals there must be a 6 somewhere
so x can’t be it because it need to be bigger than 7 (France has the fewest gold medals)
so anything bigger than x is not a possible answer.
This leaves us with 25-2x, 22-2x and 18-x.
25 - 2x must be bigger than 22-x so there is only 22-2x and 18-x left.
If it was 18-x it would mean that x = 12 and 2x = 24,
22 - 24 doesn’t make sense.
22-2x must be 6.
22 – 6 = 16
so 2x = 16 and x is 8 .
My idea was then proved right and this was my final table:
GOLD SILVER BRONZE
France 7 16 18
Italy 8 9 10
Japan 9 6 10