I have the following set of data across 28 days. I want to show that the rate at which the data from group H decrease is greater than the one in group I, however since they have a different order of magnitude this is not easily displayed. Is there a way to transform my data in order to have them at the same magnitude, i.e. have the same starting values.
You are asking for two different things.
If you want them to all start at the same $y$ value then just subtract the appropriate constant from each curve to achieve that.
If you want to show the rates of decline then take logs and the parallelism (or otherwise) of the resultant curves will show you if they have the same rate of change.