Well first, let's find the total area of the back yard. Given the dimensions, we can assume the yard is rectangular.
Area = 21.8(12) = 261.6ft²
Now we can find the area that will need to be seeded by subtracting the area of the garden from the total area:
261.6 - 34.56 = 227.04ft²
Finally, we can divide this area by 16ft² to find the number of bags of seed we will need.
227.04 ÷ 16 = 14.19 bags or little more than 14 bags.. Looks like we better buy 15 bags of grass seed to do the job..