Given:

\(p=54\%=0.54\)

\(n=8\)

Definiton binomial probability:

\(\displaystyle{P}{\left({X}={x}\right)}=\frac{{{n}!}}{{{x}!{\left({n}-{x}\right)}!}}\cdot{p}^{{x}}\cdot{\left({1}-{p}\right)}^{{{n}-{x}}}\)

Complement rule:

\(\displaystyle{P}{\left(\neg{A}\right)}={1}-{P}{\left({A}\right)}\)

Addition rule for disjoint or mutually exclusive events:

\(P(A or B)=P(A)+P(B)\)

Evaluate the definition of binomial probability at \(x=6\):

\(\displaystyle{P}{\left({X}={6}\right)}=\frac{{{8}!}}{{{6}!{\left({8}-{6}\right)}!}}\cdot{0.54}^{{6}}\cdot{\left({1}-{0.54}\right)}^{{{8}-{6}}}={28}\cdot{0.54}^{{6}}\cdot{0.46}^{{2}}\approx{0.1469}\)

Result 0.1469