A firm has net working capital of $640. Long-term debt is $4,180, total assets are $6,230, and fixed assets are $3,910. What is the amount of the total liabilities

Net Working Capital = Current Assets - Current Liablities.
Since it is given that the total assets amount to 6,230 and that the fixed assets(noncurrent assets) are 3,910; it is possible to get the current assets. You must deduct the amount of fixed assets from the total assets and that will now be your Current Assets.
After getting the Current Assets amount, you can now solve for the missing current liabilities in the net working capital formula. It is stated that the working capital is equal to 640 so again, you must deduct this amount to the Current assets to get the Current Liablities.

Since the Current liabilities amount and the Noncurrent Liabilities(long term debt) are already known, you can simply add the two to get the total liabilities amoun.

=5,860

Karrentasset's answer is correct, but needs to be justified:

Total assets 6230
Non current assets (3910)
Current assets 2320
Net current assets (640)
Current liabilities 1680
Long term liabilities 4180
Total liabilities 5860