Theory:

     And yet the man knew a great deal about him. How? He even seemed to know some intimate details. The bag of books, wife’s death, brother’s insanity... The only mistake was about his having gone to Ranchi. Not a mistake; a deliberate lie. In ’58, during the Pujas, he was in Kanpur at his friend Haridas Bagchi’s place. All Bepin Babu had to do was write to — no, there was no way of writing to Haridas. Bepin Babu suddenly remembered that Haridas had left with his wife for Japan some weeks ago, and he didn’t have his address.
 
     But where was the need for proof? He himself was fully aware that he hadn’t been to Ranchi — and that was that.
Explanation:
 
Bepin's mind was confused a bit though he was sure that he had not gone to Ranchi. The confusion on his mind is about the intimate details that the stranger had spoken about him. Bepin was confused about how Parimal Ghose had known about his personal details, such as his bookbag, his wife's death, and his brother's illness.

However, Bepin's mind accepted all details said by Ghose to be accurate except the Ranchi trip incident, for Bepin was confident and conscious that he had never been to Ranchi. Therefore, he also concluded that Parimal's talk was not the result of miscommunication but rather a deliberate falsehood regarding Ranchi.

Bepin clearly remembered visiting his friend Haridas Bagchi in Kanpur for the Pujas in October 1958. So, Bepin Babu decided to write to his friend Haridas. But it was impossible since Haridas had just taken a trip to Japan with his wife, and Bepin didn't know Haridas's address.
 
On the other hand, proof becomes unnecessary for Bepin as he was pretty much sure about not having gone to Ranchi in his life before. Therefore, when Bepin himself became absolutely conscious that he hadn't been to Ranchi, he did not want to think more about the bookstall incident.
 
Meaning of difficult words:
 
S.No
Words
Meaning
1.
InsanitySevere medical illness
2.
Miscommunication A failure to communicate clearly
3.
Absolutely Completely
4.
Falsehood A statement that is not true
Reference:
National Council of Educational Research and Training (2008). Honeydew. Bepin Choudhury’s Lapse of Memory- Satyajit Ray (pp. 59-69). Published at the Publication Division by the Secretary, National Council of Educational Research and Training, Sri Aurobindo Marg, New Delhi.