I've changed my computer just few days ago, when I've tried to reinstall Lightroom 6 a popup appeared saying that I've exceeded the number of computers linkable to that serial. I don't have the access to that computer because it's not working anymore, there's some way to reset license usage from any previous computer so that i may link that serial to my actual pc?
You cannot do this yourself. You need to contact Adobe customer service. Tip: start the conversation by saying you need to "Reset activation count". Use these exact words. This is to avoid getting into a discussion about whether old software versions are supported.