Answer
Graphing as instructed, we see that
the graph of (b) is obtained by
vertically compressing the graph of (a) by factor $\displaystyle \frac{1}{3}$
reflecting about the x-axis gives graph (c), and
shifting 4 units to the right produces graph (d).
Work Step by Step
Taking
(a) $y=f(x)=x^{6},$ we find that
(b) $y=\displaystyle \frac{1}{3}f(x),$
(c) $y=-[\displaystyle \frac{1}{3}f(x)]=-\frac{1}{3}f(x)$
(d) $y=-\displaystyle \frac{1}{3}f(x-4)$
So,
the graph of (b) is obtained by
vertically compressing the graph of (a) by factor $\displaystyle \frac{1}{3}$
reflecting about the x-axis gives graph (c), and
shifting 4 units to the right produces graph (d).