Okay, let's tackle this math problem. We're starting with 378623 and subtracting 35390.

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

Step 2: We'll start by subtracting the digit 9 and the borrow 0 from 2 in column 2 and get -7.
We add -7 to 10 and get 3 as the next digit of the result.

Step 3: We'll start by subtracting the digit 3 and the borrow 1 from 6 in column 3 and get 2.
2 is the next digit of our result.

Step 4: We'll start by subtracting the digit 5 and the borrow 0 from 8 in column 4 and get 3.
3 is the next digit of our result.

Step 5: We'll start by subtracting the digit 3 and the borrow 0 from 7 in column 5 and get 4.
4 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, 378623 - 35390 = 343233.