Let's translate these sentences to math one-by-one.
"The sum of three numbers is 62..." translates to the expression:
? + ? + ? = 62
We aren't given any modifications to the first number, so let's just pick a variable n to represent it.
n + ? + ? = 62
The second number is "equal to the first number diminished by 4. We can interpret "diminished by 4" as meaning "subtracted by 4," so we now have:
n + (n - 4) + ? = 62
And finally, we have that the third number is "four times the first," which evidently implies multiplication of the first number by 4. Which gives us:
n + (n - 4) + (4n) = 62
At this point, we don't even need to solve for n, since we already have our three expressions, and those are n, n - 4, and 4n.