Question 981366
Look at the possible working combinations 
1.A working, D working, B working, C not working
2.A working, D working, C working, B not working
3.A working, D working, B working, C working
Those are the only possible combination for which the machine works.
Find the probability of each case by multiplying probabilities together.
{{{P[1]= 0.8(0.6)(0.8)(0.4)=0.1536}}}
{{{P[2]= 0.8(0.6)(0.6)(0.2)=0.0576}}}
{{{P[3]= 0.8(0.6)(0.8)(0.6)=0.2304}}}
So then,
{{{P=P[1]+P[2]+P[3]}}}
{{{P=0.1536+0.0576+0.2304}}}
{{{P=0.4416}}}