way of saying: 'to aknowledge something coming at you, both literally and metaphorically, in a quick way because life is short and you gotta think fast!'
"Think with your balls" means think smart or outside the box. To think with your balls is usually a very quick and instinctive way of making decisions. It derives from the show "How Not To Live Your Life" A decision made by the balls is often a very good short term solution to a problem but will cause trouble in the future.
"What shall we do with all the orphans?"
"Sell them on, make a tidy profit."
"Thats amazing, how did you think of that! Now were making loads of money."
"Well, you have to think with your balls."