Know the book but don't have a current version.
It's impossible for anyone else to tell you why a trial balance is out of balance without seeing all the work you did. This does create a difficulty if someone can't sit down with you in person. Sometimes I can spot obvious things, if you would put whether these are all dr & cr, and what your totals are.
A process you can do though. First, re-add the columns. Should go without saying, but sometimes people freak when it doesn't balance and don't think of that. Then figure out the difference between the two columns. Look for that number somewhere. You may have just left something out. Then divide the difference in two. When something gets put on the wrong side, the error doubles itself. For instance, if you should have debited $50 and you credited instead, you will actually be $100 off. So if you take the $100 error and divide in two, there you have your $50 that you can look for. You can also see if the difference is divisable by 9, which may indicate two numbers flipped. (i.e. 543 instead of 453.) I don't find that useful since it only means it might be two numbers flipped, and you still have to look carefully to find it.
If none of those work, start working backwards. i.e. the last thing done was to copy from the accounts. So check that everything was copied correctly, in the right place, all numbers right, and didn't miss anything. Then check each individual account that all the math is correct.
If you did journal entries and posted them (as opposed to journalizing straight into t accounts, as some problems have you do), then you may have to check all the postings, which is a tedious hassle and best left as a last resort. And this has to be done very carefully. Oh, and make sure all the entries balance to begin with.
One common posting problem I see is when something has been corrected after it's already been posted. For instance, you debited cash when you should have debited receivables. The cash has already been posted. So you correct the entry to receivable, post it, but never un-post the cash. That type of thing can cause all sorts of problems.
Besides good luck, I can only say one thing, which I cannot stress enough: be very, very careful about all your work as you go along, to try to prevent things not balancing when you get done. A lot of people are not good at this tedious stuff, but you have to be careful with everything you do. Trying to track it later is even worse.
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