6. (10 points) Two cubes of different sizes are glued together to form the solid figure shown below, where the four vertices of the smaller cube's bottom face are exactly the midpoints of the edges of the larger cube's top face. If the edge length of the larger cube is 2, then the surface area of this solid figure is . $\qquad$
【Analysis】As shown in the figure,
since the four vertices of the bottom face of the small building block are exactly the midpoints of the edges of the top face of the large building block, the area of one face of the large cube is twice the area of one face of the small cube. Therefore, the surface area of this solid figure is the surface area of the large cube plus the area of four faces of the small cube. Solve accordingly.

【Solution】Solution: $6 \times 2 \times 2+4 \times(2 \times 2 \div 2)$
$$
\begin{array}{l}
=24+4 \times 2 \\
=24+8 \\
=32 .
\end{array}
$$

Answer: The surface area of this solid figure is 32.
Therefore, the answer is: 32.