Step 1: Geometry of \( [CoCl_2(NH_3)_4] \).
This complex has coordination number:
\[
6
\]
Coordination number \(6\) generally gives:
\[
\text{Octahedral geometry}
\]
So:
\[
A-I
\]
Step 2: Geometry of \( [Co(NH_3)_6]Cl_3 \).
The complex ion is:
\[
[Co(NH_3)_6]^{3+}
\]
It has six ammonia ligands.
Thus, coordination number is:
\[
6
\]
So geometry is:
\[
\text{Octahedral}
\]
Therefore:
\[
B-I
\]
Step 3: Geometry of \( [NiCl_4]^{2-} \).
Nickel with chloride ligands usually forms a tetrahedral complex in:
\[
[NiCl_4]^{2-}
\]
So:
\[
C-IV
\]
Step 4: Geometry of \( [Fe(CO)_5] \).
Iron pentacarbonyl has coordination number:
\[
5
\]
The geometry of:
\[
[Fe(CO)_5]
\]
is:
\[
\text{Trigonal bipyramidal}
\]
So:
\[
D-II
\]
Therefore, the correct matching is:
\[
A-I,\quad B-I,\quad C-IV,\quad D-II
\]