Given,
$$
A=\left[\begin{array}{cccc}
1 & 1 & -1 & 0 \\
4 & 4 & -3 & 1 \\
b & 2 & 2 & 2 \\
9 & 9 & b & 3
\end{array}\right]
$$

For rank to be 3, there must exist 3 non zero row. Now, applying $R_2 \rightarrow R_2-4 R_1 ; R_3 \rightarrow R_3-2 R_1$
$$
=\left[\begin{array}{cccc}
1 & 1 & -1 & 0 \\
0 & 0 & 1 & 1 \\
b-2 & 0 & 4 & 2 \\
9 & 9 & b & 3
\end{array}\right]
$$

Applying $R_4 \rightarrow R_4-9 R_1$
$$
=\left[\begin{array}{cccc}
1 & 1 & -1 & 0 \\
0 & 0 & 1 & 1 \\
b-2 & 0 & 4 & 2 \\
0 & 0 & b+9 & 3
\end{array}\right]
$$

Again, applying $R_4 \rightarrow R_4-3 R_2$
$$
A=\left[\begin{array}{cccc}
1 & 1 & -1 & 0 \\
0 & 0 & 1 & 1 \\
b-2 & 0 & 4 & 2 \\
0 & 0 & b+6 & 0
\end{array}\right]
$$

If rank $=3$, then
Last row must have all elements 0 .
$$
\therefore \quad b+6=0 \Rightarrow b=-6
$$