Explanation:
last week they ate 1 1/6 = 6/6 + 1/7 = 7/6 cartons.
this week they ate 3 = 3×6/6 = 18/6 cartons.
so, how much more did they eat ?
it is not fully clear to me, if we need to find the absolute difference in cartons, or if we need the factor between both amounts (like "how many times did they eat more ?").
to be safe I give you both.
in absolute difference :
18/6 - 7/6 = 11/6 cartons = 1 5/6 cartons more.
as factor :
7/6 × x = 18/6
7x = 18
x = 18/7
they ate 18/7 = 2 4/7 times more