How to calculate retained earnings balance as of June 2004 if retained earnings for June 2005 is said to be 60,000 and decrease total liability during 2005 is said to be 20,000 and the gain from sale of boats during 2005 is 15,000 and dividends declared and paid during 2005 is 2000 and proceeds from the sale stock in 2005 is 62,000 and the net income for the year that ended in June 2005 is 35,000

Let's first separate out what affects retained earnings and what does not.

Retained earnings is beginning balance + net income - dividends = ending balance.

You have 3 of those 4 numbers outright given to you. All you need do is plug them in, work backwards and you'll have your beginning balance.

The trick here is ignoring all the junk they gave you that isn't needed. Are liabilities in the above equation? And "net income" is the bottom-line net income with everything already in it. It doesn't say operating income. It says net income. All items affecting net income should already be in that number and you shouldn't have to do anything with them at all.

See if you can get it from there.