Note: If P(Hector is hired) = 1/3, then P(Hector is NOT hired) = 2/3

If Hector is hired before the end of Wednesday, and that means Hector was hired on Monday OR on Tuesday OR on Wednesday.
Rather than consider all three possible cases, we can save some time by using the complement.
That is: P(hired before end of Wednesday) = 1 - P(NOT hired before end of Wednesday)

P(NOT hired before end of Wednesday)
P(NOT hired before end of Wednesday) = P(NOT hired on Monday AND NOT hired on Tuesday AND NOT hired on Wednesday)
= P(NOT hired on Monday) x P(NOT hired on Tuesday) x P(NOT hired on Wednesday)
= 2/3 x 2/3 x 2/3
= 8/27

So, P(hired before end of Wednesday) = 1 - 8/27
= 27/27 - 8/27
= 19/27

Answer: D