To explain his design to his visitor, the architect . . . . . . . . a simple plan on the blackboard.

The correct answer is (C). The architect sketched a simple plan on the blackboard.

To construct something means to build it or put it together. To make something means to create it or produce it. To build something means to construct it or erect it. To sketch something means to draw it roughly or in outline.

In this case, the architect is trying to explain his design to his visitor. He does this by sketching a simple plan on the blackboard. This is the best way to communicate his ideas visually and to get his point across quickly.