Step 1: Note the two clues.
The explorer is Italian and the dates are 1623 and 1624. Both clues must match for an option to be right, so we test the nationality first and the dates next.
Step 2: Use the nationality clue.
Akane Yamaguchi sounds Japanese, Victor Axelson sounds Scandinavian and Antony Atkinson is an English name. Only Pietro Della Valle is an Italian name. This already leaves one option.
Step 3: Confirm with history.
Della Valle landed at Surat in 1623, went down the western coast and reached Goa and Calicut. His letters, called Viaggi, are a valued source on Indian towns, trade and customs of that time.
Step 4: Choose the option.
The name and the dates both match option 1, so the other three are dropped.
Step 5: Second check.
A useful memory aid is that Della Valle belongs to the group of European travellers of the early Mughal age, like Thomas Roe from England and Peter Mundy. Each wrote about India for readers at home. The other three names in the list are not part of this group of known travellers. Checking both the name and the date again gives the same result, option 1, with no doubt left.
Final Answer:
Pietro Della Valle is the Italian traveller, so option 1 is correct.
\[\boxed{\text{Option 1}}\]