Two persons make a single throw with a pair of dice.The probability that their throws are unequal is? 
Two persons make a single throw with a pair of dice.The probability
  that their throws are unequal is ?

How should I calculate the number of ways in which the throw can be equal?

Probability that the sums are equal breaks into $11$ disjoint cases: Equal sums of $2$, equal sums of $3$,..., equal sums of $12$.
$P($ both sums equal 2$)=\left(\frac{1}{36}\right)^2$
$P($ both sums equal 3$)=\left(\frac{2}{36}\right)^2$
etc.
Add up the probabilities of all the cases, then subtract from $1$ to get the desired complementary probability that the sums are unequal.
