The sum of the ages of two brothers is 46. the younger brother is 10 more than a third of the older brother's age. how old is the younger brother ?

Let's try to do this with a little guess and check.
We'll use numbers easily divided by 3 for the older brother's age.
If the older brother is 30, the younger brother is 16.  (30 + 16 = 46)
Now, we check that with the 10 + 1/3 the older brother's age.
30 ÷ 3 = 10
10 + 10 = 20
20 > 16
That one doesn't work.
Let's try 24 for the older brother's age.
That means the younger brother would be 22, because 24 + 22 = 46.
24 ÷ 3 = 8
8 + 10 = 18
18 < 22
That one doesn't work, either.
We'll try one more. If the older brother is 27, the younger brother would be 19. (27 + 19 = 46)
27 ÷ 3 = 9
9 + 10 = 19
19 = 19
This one fits all the requirements of the problem.
That means that the answer to the question of "how old is the younger brother?" is
The younger brother is 19 years old.