[tex]y = 4^x \quad \to\quad y = - \frac 2 3 (4^{x+7}) - 5[/tex]
[tex]y=4^x[/tex]
OK, we'll go in steps. First a reflection through the x axis, which negates y.
[tex]y = -4^x[/tex]
Now a vertical scaling of 2/3
[tex] y = -\frac 2 3 \cdot 4^x[/tex]
Now we shift seven units to the right,
[tex] y = -\frac 2 3 \cdot 4^{x+7}[/tex]
Now down five,
[tex] y = -\frac 2 3 \cdot 4^{x+7} - 5[/tex]
There it is.
Answer: reflection thru x axis, vertical scale 2/3, right shift 7, down 5, second choice
