It's taken me a while to get my head around that but here's how I read it:
Firstly, they've stated that if the extension didn't exceed three metres from the rear wall of the house it would be a 'permitted development' and therefore not require planning permission.
https://www.planningportal.co.uk/info/200130/common_projects/17/extensions
By the planning authority's way of measuring things though, they've calculated the measurement as 3.9m and therefore correctly stated that they recognise the need for planning approval.
However they've then gone on to grant such consent anyway.
So I can't see that any conditions have been imposed. All that you're reading is an explanation of the planning authority's way of working. (i.e. Step 1: Determine whether or not the proposal is actually a 'permitted development', which doesn't even need planning permission anyway. Step 2: Explain why planning consent is needed and then decide whether or not to grant it).