Correct Answer - Option 2 : 19
th March
The logic followed here is,
P's first appointment to the job is after 17th but before 20th March.
Two date for between 17th but before 20th March → 18th march and 19th march.
And,
B remembers that P's first appointment to the job is after 18th but before 22nd March.
Three date between 18th to 22nd March → 19th march, 20th march and 21 march.
There are common date is 19th March.
So, 19th march is most likely to be P's first appointment to the job.
Hence, correct answer is 19th march.