Let's denote the ages of the two remaining men as x and x + 3 (since one is 3 years older than the other).
We know that the average age of 6 men is 35 years. So, the sum of their ages is 6 * 35 = 210 years.
We also know that the average age of four of them is 32 years. So, the sum of their ages is 4 * 32 = 128 years.
To find the sum of the ages of the two remaining men, we subtract the sum of the ages of the four men from the sum of the ages of all six men:
210 - 128 = 82 years.
Now, we can set up an equation to solve for the ages of the remaining two men:
x + (x + 3) = 82.
Combining like terms, we get:
2x + 3 = 82.
Subtracting 3 from both sides:
2x = 79.
Dividing both sides by 2:
x = 39.5.
So, one of the remaining men is 39.5 years old, and the other is 39.5 + 3 = 42.5 years old.