A box weighing 660 N is sliding across a cement floor and the coefficient of sliding friction between the box and the floor is 0.15. If the force pushing the box is 500 N, what is the acceleration of the box?

To find the acceleration of the box, we can follow these steps:

1. **Calculate the force of friction (F_friction)**:
The force of friction can be calculated using the formula:
\[
F_{\text{friction}} = \mu \cdot F_{\text{normal}}
\]
where \(\mu\) is the coefficient of sliding friction and \(F_{\text{normal}}\) is the normal force. For a box on a horizontal surface, the normal force is equal to the weight of the box (the gravitational force acting on it).

Given:
\[
\mu = 0.15
\]
\[
F_{\text{normal}} = 660 \, \text{N}
\]

Now we can calculate the force of friction:
\[
F_{\text{friction}} = 0.15 \cdot 660 \, \text{N} = 99 \, \text{N}
\]

2. **Determine the net force (F_net)**:
The net force acting on the box can be found by subtracting the force of friction from the pushing force:
\[
F_{\text{net}} = F_{\text{push}} - F_{\text{friction}}
\]

Given:
\[
F_{\text{push}} = 500 \, \text{N}
\]

Substituting in the values:
\[
F_{\text{net}} = 500 \, \text{N} - 99 \, \text{N} = 401 \, \text{N}
\]

3. **Calculate the acceleration (a)**:
To find the acceleration, we use Newton's second law:
\[
F_{\text{net}} = m \cdot a
\]
where \(m\) is the mass of the box. First, we need to find the mass of the box using the weight (weight = mass × gravity):
\[
F_{\text{gravity}} = m \cdot g
\]
where \(g\) is the acceleration due to gravity (approximately \(9.81 \, \text{m/s}^2\)).

Thus, the mass \(m\) can be calculated as:
\[
m = \frac{F_{\text{gravity}}}{g} = \frac{660 \, \text{N}}{9.81 \, \text{m/s}^2} \approx 67.14 \, \text{kg}
\]

Now we can find the acceleration:
\[
a = \frac{F_{\text{net}}}{m} = \frac{401 \, \text{N}}{67.14 \, \text{kg}} \approx 5.96 \, \text{m/s}^2
\]

4. **Round the acceleration**:
The calculated acceleration is approximately \(6 \, \text{m/s}^2\).

Thus, the answer is:

**D. 6 m/s²**