The constant 12 can be taken outside the summation because it applies to every term. The series becomes:
12(-1/5+1/25-1/125+1/625-...). The series is a GP with common factor r=-1/5. the series can be written -(12/5)(1-1/5+1/25-...). Call the series in brackets S. So S=1-1/5+1/25-...+5^-n. Therefore S/5=1/5-1/25+...+5^-(n+1) and S+S/5=1+5^-(n+1). When n is very large 5^-(n+1) becomes very small, and it doesn't matter whether it's positive or negative, so we can say that as n approaches infinity the term becomes 0. Therefore S+S/5=6S/5=1 and S=5/6.
Returning to the original GP, we have -(12/5)S=-12/5*5/6=-2. So the series converges to -2.