I am trying to find the amount of liabilities for December 2014, given assets for 2014 119,000 and December 2015 assets 113,000, liabilities 70,000, owner investments 6,500, net income 20,000 and owner withdrawals 11,000.

First you have to calculate the Owners Equity at Dec 2015 (Ending), which is the basic accounting equation rewritten to: Assets - Liabilities = Owners Equity. So take your 2015 assets minus 2015 liabilities to get 2015 owners equity.

Now you have to solve for Dec 2014 (beginning) owners equity. To do this you have to know the changes in equity formula, which is;
Beginning Owners Equity + Owner Investments - Owner Withdrawals + Net Income(Revenues - Expenses) = Ending Owners Equity

Since you have all the amounts needed except Beginning Owners Equity you can rewrite the formula to solve for the missing amount. So:
Ending Owners Equity - Owner Investments + Owner Withdrawals - Net Income = Beginning Owners Equity

Finally you have the Dec 2014 amounts needed to solve for 2014 Liabilities. The basic accounting equation rewritten to:
Liabilities = Assets - Owners Equity

Just use your 2014 amounts to solve for liabilities.