right click the folder, select properties and then the repair button. Do the numbers match now?

I really don't know what a chain is, but if you are asking if a reply is noted as belonging to the thread it was replied from then the answer is yes.

Thanks but 'repair' makes no difference. I have (7) showing for the inbox folder after I have opened everything. An addition to my chain/thread only appears on the original email - maybe months old. There is no fresh indication that anything has arrived, so no alert to open the original. Graham.

I took a guess because I have no idea where this 6/7 or 3/3 comes from.

My accounts simply show a number as shown here

With the actual number of unread messages whown in brackets. Sometimes there is a down arrow prefix to indicate the number shown includes sub folders that are not visible. You can see that against the archive folder.

Likewise I have no idea what a "chain is". It I assume it is a thread, which is discussed here https://support.mozilla.org/en-US/kb/message-threading-thunderbird

If that is the case, if you click reply or forward the email wll contain appropriate references to be added to the thread.

OK the inbox numbers don't matter too much but the thread issue remains - for example:

I ordered new fencing last July. The firm confirmed by email but said it would mean a long wait. In December they offered a date by adding to the July email. I had no idea anything had been added. I lost several months of waiting. Should not the thread also result in an an alert, so that I can go back to the first email???? Cheers, Graham.