a way/bypass to get around an obstacle/problem
a way to stretch/bend the rule
「变通」这个词其实是「穷则变，变则通 (语出《易经》)」这个说法精简而来的。The phrase 变通 is actually reduced from a longer version from I-ching: 穷则变，变则通.
The 穷 here doesn't mean "poor", as in poverty. It means "without a way out".
So the whole thing means "When there isn't a way out, make a change. Making a change will get you a way out." And 变通 is just a shorter version of 变则通. Hence, 变通之道 is a way to finding a way out.
想吃顿好饭，又不想花太多钱，有什么变通之道？I want to have a decent meal but don't want to spend much; is there any roundabout way to achieve that?
经济不景气让许多企业苦思变通之道。Slow economy leaves many business struggling to find out a way to survive.