First of all, we have that the sum of all the odd integers from 28 to 46 are 29 + 31 + ... + 43 + 45. That is a total of 9 numbers.
Let's represent this sum as a variable s:
s = 29 + 31 + ... + 43 + 45
Then reverse the order:
s = 45 + 43 + ... + 31 + 29
Add these two each other:
s + s = (29 + 45) + (31 + 43) + ... + (43 + 31) + (45 + 29)
s + s becomes 2s. Notice, from the left to right of the first two terms. As 29 increases by 2 to become 31, we can see that 45 also decreases by 2 to become 43. Since this goes on all the way, this means that essentisally, all of these terms are the same:
29 + 45 = 31 + 43 = ... = 43 + 31 = 45 + 29
And since there are 9 of them, we could just sum one of these terms and multiply by 9:
2s = (29 + 45) * 9 = 74 * 9 = 666.
Finally, we divide both sides by 2:
{2s}/2 = 666/2
s = 333