Each match has 3 possible outcomes.
For 11 matches,on total there are $3^{11}$ ways of prediction.
for each match,probability that our prediction is correct is 1/3.
Hence the probability that our prediction is wrong is 2/3.
Let X be the random variable that counts number of correct predictions.
therefore P(X=6)=$\binom{11}{6}$*$\left ( 1/3 \right )^{6}$*$\left ( 2/3 \right )^{5}$.(by Binomial theorem)
Total number of ways in which exactly 6 predictions are correct= probability that exactly 6 predictions are correct*Total number of predictions.
=$\binom{11}{6}$*$\left ( 1/3 \right )^{6}$*$\left ( 2/3 \right )^{5}$ * $3^{11}$.
=$\binom{11}{6}$ * $2^{5}$