Dear Student
Goodwill is an asset, Now we know assets are equal to liabilities and whenever we write off any asset i.e we reduce the balance of assets means the liabilities or capital shall also be reduced in any manner.
Therefore goodwill, when written off, reduces the capital as well.
In case of reconstitution, fresh goodwill is valued therefore old goodwill is written off which is appearing in the balance sheet.
Regards