To solve for retained earnings, you have to add the net income from the beginning retained earnings then deduct dividends.
Based on the problem, these are the given:
Beginning Retained Earnings = $150,000
Net Income = $75,000
Cash Dividend = $45,000
Stock Dividend = $15,000
$150,000 + $75,000 - $60,000 = $165,000 is the retained earnings available for dividends at the end of 2011