This problem is taken from Hoffman kunz linear algebra section $5.3$ page no $155$
Let $\sigma$ and $\tau$ be the permutations of degree $4$ defined by
$$\sigma1= 2, \sigma2= 3,\sigma3= 4, \sigma3= 4$$
$$\tau1=3,\tau2=1,\tau3=2,\tau4=4$$
$(a)$ Is $\sigma$ odd or even? Is $\tau $ odd or even?
My attempt :$\sigma1= 2, \sigma2= 3,\sigma3= 4, \sigma3= 4 \implies \begin{pmatrix}1&2&3&4\\2&3&4&1\end{pmatrix}$
$$\sigma=(1234)$$
$$\sigma=\underbrace{(1234)}_{4 \text{number}}$$
$4$ is even $\implies \sigma$ is even
similarly $\tau=(132)$ ,$\tau=\underbrace{(132)}_{3 \text{number}}$ $3$ is odd implies $\tau$ is odd
Well, the first issue here is that you need to look up the definition of odd and even permutations. Look through the answers on this question for that.
If you need help breaking up the permutations into transpositions look at the accepted answer here.
Can you take it from here?