I'm having trouble calculating missing information (liabilities).
Dec 31, 2010
Assets: 123,000 Liabilites? Equity?
Dec 31, 2011
Assets 112,500 Liabilites 75,000 Equity 37,500
During year 2011:
Stock issuances of 4,500, Net income of 18,000 and cash dividends of 9,000

What is the amount of liabilites on Dec. 31, 2010?

You have ending 2011 equity and different information during 2011, so just reverse the information during 2011 or back track to get your beginning 2011 equity(also known as ending 2010 equity).

Start with your ending 2011 equity, subtract your stock issuances during the year, subtract your net income during the year, and add your cash dividends during the year to get your ending 2010 equity.

Once you have your ending 2010 equity just subtract from your ending 2010 assets to get your ending 2010 liabilities.