Step 1: Assign charges.
- Let oxidation state of Ni = $y$.
- Each CN$^-$ ligand carries a charge of –1.
- Total number of ligands = 4.
Step 2: Write the charge balance equation.
\[
y + 4(-1) = x
\]
Step 3: Consider Ni oxidation state.
Nickel generally shows +2 oxidation state in complexes. So, $y = +2$.
Step 4: Substitute values.
\[
(+2) + 4(-1) = x
\]
\[
2 - 4 = -2
\]
\[
x = -2
\]
Step 5: Final Answer.
Hence, the value of $x$ in [Ni(CN)$_4$]$^x$ is –2.
\[
\boxed{-2}
\]