Although 'can' is the modal of ability, it is often used these days instead of 'may' to talk about permission.
'I hope we will be allowed to build an extention to our house.' means
I hope we can get permission to do so (from the authorities for example.)
'I hope we are able to (or can) build an extention to our house.' means
I hope we have the ability to do so, that is, we have enough money, enough skill etc.)
When we say, 'I hope we can build an extention to our house'
we may actually mean we hope we will be allowed to do.
Our meaning will usually be clear from the context.
- For Teachers