Answer
See below
Work Step by Step
A $3 × 8$ matrix $A$ has $rank(A)+nullity (A)=8$
Since $A$ has $3$ rows, $rank (A) \leq 3\\
\rightarrow nullity (A) \geq 5$
Since nullity (A) is a subspace of $R^8$, then $nullity (A) \leq 8$
An example of a $3 × 8$ matrix $A$ with $nullity(A) = 5$
$\begin{bmatrix}
1 & 0 &0 & 0 & 0& 0 & 0 & 0\\
0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\
0 & 0 & 1 & 0 & 0 & 0 & 0 & 0
\end{bmatrix}$
A $3 × 8$ matrix A with $nullity(A) = 8$ is $0_{3\times 8}$
