If I had at the beginning of the year a total asset of 800,000 and total liability of 500,000 and during the year assets increased to 150,000 and liability decreased by 80,000 what would the owner's equity be at the end of the year.

You need to know the accounting equation, which is: Assets = Liabilities + Owners Equity

This equation can be rewritten as: Owners Equity = Assets - Liabilities

Now start with your assets of $800,00 + 150,000 equals your ending year assets.

Also start with your liabilities of $500,000 - 80,000 equals your ending year liabilities.

Once you have your ending year amounts for assets and liabilities, just plug-in your numbers into the equation above and solve for ending year owners equity.