Geetha wants to cut a cube of size $4 \times 4\times 4$ into $64$ unit cubes (of size
$1\times 1\times 1$). Every cut must be straight, and parallel to a face of the big cube. What
is the minimum number of cuts that Geetha needs?
Note: After every cut, she can rearrange the pieces before cutting again. At every
cut, she can cut more than one pieces as long as the pieces are on a straight line.
To solve this problem, we need to determine the minimum number of straight cuts required to divide a $4 \times 4 \times 4$ cube into $64$ unit cubes of size $1 \times 1 \times 1$. 

1. **Initial Setup**:
   - The large cube has dimensions $4 \times 4 \times 4$.
   - We need to cut it into $64$ smaller cubes of dimensions $1 \times 1 \times 1$.

2. **Understanding the Cutting Process**:
   - Each cut can be made parallel to one of the faces of the cube.
   - After each cut, the pieces can be rearranged before making the next cut.

3. **First Dimension Cuts**:
   - To divide the cube along one dimension (say along the $x$-axis), we need to make 3 cuts. This will divide the cube into 4 slices along the $x$-axis.
   - After 3 cuts, we have $4 \times 4 \times 4$ slices.

4. **Second Dimension Cuts**:
   - Next, we need to divide each of these slices along the $y$-axis. Again, we need 3 cuts to divide each slice into 4 smaller slices along the $y$-axis.
   - After these 3 additional cuts, we have $4 \times 4 \times 4$ smaller pieces.

5. **Third Dimension Cuts**:
   - Finally, we need to divide each of these smaller pieces along the $z$-axis. We need 3 cuts to divide each piece into 4 unit cubes along the $z$-axis.
   - After these 3 additional cuts, we have $4 \times 4 \times 4$ unit cubes.

6. **Total Number of Cuts**:
   - We made 3 cuts along the $x$-axis, 3 cuts along the $y$-axis, and 3 cuts along the $z$-axis.
   - Therefore, the total number of cuts required is $3 + 3 + 3 = 9$.

Thus, the minimum number of cuts required to divide the $4 \times 4 \times 4$ cube into $64$ unit cubes is $9$.

The final answer is $\boxed{9}$.