How do you graph y=\frac{1}{2} \cdot 4^x?

Step 1: Sketch the graph of $y = {4}^{x}$. (Since its base is greater than 1, its graph is increasing.)
Step 2 Vertically shrink the graph in Step 1 by a factor of $2$.
The graph in solid blue is the graph of $y = \frac{1}{2} \cdot {4}^{x}$.