Lets assume: Francesca has X number of balls  -------A

Then Chiara has X+3 Balls  (because chiara has 3 balls more than Francesca) ---------B

Marco has X+3+7    (because Marco has 3 balls more than Chiara) ----------C

Therefore Francesca, Chiara and Marco has total X+X+3+X+3+7 balls  (which is A+B+C)
 which is equal to 46 (as it said in the statement)

Therefore, X+X+3+X+3+7=46

or, 3X+13=46

or, 3X=46-13

or, 3X=33

or, X=33/3=11

Now we know the value of X

Therefore, Francesca has X=11 balls ( from our initial assumption A)

Chiara has X+3=11+3=14 balls         (from assumption B)

Marco has X+3+7=11+3+7=21 balls   (from assumption  C)

Answer: Francesca has 11 balls, Chiara has 14 balls and Marco has 21 balls