Let the packages with 12 donuts be x and let the ones with 6 donuts be y.

In that case, we can say that y + 2 = x because there are two more 12 donut packages than there are 6 donut packages.

We can also say that  12 x + 6y = 114 because the total number of donuts is made up of the number of 12 packs (x) times 12 (donuts per pack) plus the number of 6 packs (y) times 6.

So now we subsititute the first equation into the second

12 (y + 2) + 6y = 114

12y + 24 + 6y = 114

18 y = 90

y = 5

So there are 5 packages of 6 donuts.  This means there must be 7 packages with 12 donuts.