The 8 punishments would be total on the account, because if it was in a short while, they would ascend the punishment tiers (10 game chat restriction, 25 game chat restriction, 14 day ban, perm ban) and have been banned earlier.
After 3-6 months of regular playing, your punishment tier generally lowers by one. Valid reports against your account make that process take longer. Not playing on an account means that it doesn't degrade.
The only way I can think of to check your punishment history is with a support ticket at : https://support.riotgames.com/hc/en-us/requests/new
They will be able to give you the details of your punishment history, but they will not tell you what punishment tier an account is currently on. It's purposefully vague to encourage people to continue to be careful with their actions instead of feeling free to be toxic because they have another punishment tier available.