Ok I figured it out. Here's how it works.
The rules are that if you pay off the entire balance (this is a big IF), then NO interest will apply. So if you manage to pay off the entire balance of $2,276 within 6 months (the deferred interest period), then you will be charged NO interest at all. However, companies know very well that the majority of the people will not be able to pay off the entire balance within 6 months. So this is when they retroactively charge interest to make a lot of money.
So Alex could have made payments to fully pay off the $2,276 debt within 6 months...BUT...Alex made payments of $112 for 6 months, which means he really only paid 6*112 = 672 dollars toward the balance and he's nowhere close to paying off the entire balance of $2,276
So here's what happens
a) Alex did make 6 payments of $112 or $672 total over 6 months. So subtract this from the initial balance to get: 2,276 - 672 = 1604. Notice how the balance is not $0. So the balance was not paid for in full. If it was $0, then Alex can walk away without having to make any more payments. It's not $0, so we move onto b)
b) Because the balance was NOT paid in full by the end of the 6 month deferment period, this means that interest is applied for every month in the 6 month deferment period. All of this is applied to the initial balance and payments are not factored in (yet).
So, P*(1+r/n)^(n*t) = 2276*(1+0.2349/12)^(12*6/12) = 2,556.74
c) The balance is now 2,556.74 dollars. This would be the final answer if Alex did not make any payments at all during this 6 month period. However, alex did make monthly payments of $112 and he paid the company $672 so far. So that is subtracted from the balance to get 2,556.74 - 672 = 1,884.74
So that explains why the remaining balance after the 6 month deferment period is $1,884.74
The same basic steps are applied to the problem with Sakura as well.