I believe you are correct.
On a cold winter morning in Alaska, the probability that Emery's car will start is 0.45 and the probability that Diana's car will start 0.62
What is the probability that neither car will start?
0.45 X 0.62 = 0.279? - both cars will start (P(A and B) = P(A) x P(B)?
0.45 x 0.38 = 0.17 - start Emery and not start Diana
0.55 x 0.62 = 0.341
0.55 x 0.38 = 0.209( that both will not start)
The probability that D's car will not start is 1-0.62=0.38
Now assuming that the cars starting /not starting are independent the probability that neither start is 0.55x0.38=0.209
Note the required assumption is so unlikely as to make the question ludicrous