To begin, make a list of all the pair of numbers that have a sum of 8.
1 + 7
2 + 6
3 + 5
4 + 4
Now, multiply those pairs together, and see which one has the largest product.
1 * 7 = 7
2 * 6 = 12
3 * 5 = 15
4 * 4 = 16
So to conclude, 4 and 4 have a sum of 8 and the greatest product, 16.