The 120/360 part is correct for each. This represents 1/3 of the circle since 120/360 = 1/3
Recall the formula to get the circumference is
C = 2pi*r
where r is the radius. The larger circle has a radius of 5+1 = 6; the smaller has a radius of 5.
The larger circle has a circumference (aka perimeter) of 2pi*r = 2pi*6 = 12pi. Take one third of this to find the larger arc and you should get 4pi.
The smaller circle has a perimeter of 10pi. One third of this is (10/3)pi which is the smaller arc length.
The difference of these arc lengths is what we're after
4pi - (10/3)pi = 2.094 approximately which rounds to 2.1 as the final answer
I used my calculator's stored value of pi rather than something like 3.14 so I could get the most accuracy possible.