Step 1: Bonding in \(C_2H_4\).
Ethene contains a carbon-carbon double bond:
\[
C=C.
\]
A double bond consists of:
\[
1\sigma+1\pi.
\]
So:
\[
A-IV.
\]
Step 2: Bonding in \(C_2H_2\).
Ethyne contains a carbon-carbon triple bond:
\[
C\equiv C.
\]
A triple bond consists of:
\[
1\sigma+2\pi.
\]
So:
\[
B-I.
\]
Step 3: Bonding in \(CH_4\).
Methane has four C--H single bonds.
Each single bond is a sigma bond.
So methane contains:
\[
4\sigma \text{ bonds}.
\]
Therefore:
\[
C-III.
\]
Step 4: Bonding in \(NH_3\).
Ammonia has:
\[
3
\]
N--H sigma bonds and one lone pair on nitrogen.
So:
\[
D-II.
\]
Therefore, the correct matching is:
\[
A-IV,\quad B-I,\quad C-III,\quad D-II.
\]