Implementing logic gates in CMOS
Yes, your solution is very nearly correct. Here are the steps, which you really should have shown in your question:

In order to deal with the second top-level term, you need to apply De Morgan's Law, which states:

$$\overline{A \cdot B} = \overline{A} + \overline{B}$$

and

$$\overline{A + B} = \overline{A} \cdot \overline{B}$$

Using this, you can make the following transformation:

$$(\overline{B + C}) \cdot D = \overline{B} \cdot \overline{C} \cdot D$$

This transforms the entire function into:

$$F = A \cdot B \cdot C + \overline{B} \cdot \overline{C} \cdot D$$

which is a normal sum-of-products expression.

In order to implement this in CMOS, however, you need a function that has an overall inversion, so you need to apply the law again:

$$F = \overline{\overline{(A \cdot B \cdot C)} \cdot \overline{(\overline{B} \cdot \overline{C} \cdot D)}}$$

and again (two places):

$$F = \overline{(\overline{A} + \overline{B} + \overline{C}) \cdot (B + C + \overline{D})}$$

Your schematic diagram is correct, but your layout does not quite match it. There are a few missing connections on the NMOS side.