Okay, let's tackle this math problem. We're starting with 345158 and subtracting 6874.

Step 1: We'll start by subtracting the digit 4 and the borrow 0 from 8 in column 1 and get 4.
4 is the first digit of our result.

Step 2: We'll start by subtracting the digit 7 and the borrow 0 from 5 in column 2 and get -2.
We add -2 to 10 and get 8 as the next digit of the result.

Step 3: We'll start by subtracting the digit 8 and the borrow 1 from 1 in column 3 and get -8.
We add -8 to 10 and get 2 as the next digit of the result.

Step 4: We'll start by subtracting the digit 6 and the borrow 1 from 5 in column 4 and get -2.
We add -2 to 10 and get 8 as the next digit of the result.

Step 5: We'll start by subtracting the digit 0 and the borrow 1 from 4 in column 5 and get 3.
3 is the next digit of our result.

Step 6: We'll start by subtracting the digit 0 and the borrow 0 from 3 in column 6 and get 3.
3 is the next digit of our result.

So, 345158 - 6874 = 338284.