What is the total number of sigma $(\sigma)$ and pi $(\pi)$ bonds in the following molecules?
$(a)$ $C_{2}H_{2}$
$(b)$ $C_{2}H_{4}$

(N/A) single bond is a result of the axial overlap of bonding orbitals. Hence,it contributes a sigma $(\sigma)$ bond.
$A$ multiple bond (double or triple bond) is always formed as a result of the sidewise overlap of orbitals,which contributes a pi $(\pi)$ bond.
$1.$ Structure of $C_{2}H_{2}$ (Ethyne): $H-C \equiv C-H$
In $C_{2}H_{2}$,there are $3$ sigma $(\sigma)$ bonds ($2$ $C-H$ and $1$ $C-C$) and $2$ pi $(\pi)$ bonds.
$2.$ Structure of $C_{2}H_{4}$ (Ethene): $CH_{2}=CH_{2}$
In $C_{2}H_{4}$,there are $5$ sigma $(\sigma)$ bonds ($4$ $C-H$ and $1$ $C-C$) and $1$ pi $(\pi)$ bond.