How I am supposed to combine these two pieces of information?
From the description of the bracers:
When worn by a paladin, he is considered four levels higher for the purposes of determining the uses per day and healing provided by his lay on hands class feature.
From the Paladin class Feature:
When a paladin reaches 4th level, she gains the supernatural ability to channel positive energy like a cleric. Using this ability consumes two uses of her lay on hands ability. A paladin uses her level as her effective cleric level when channeling positive energy.
May I deduce that the +4 from the bracers also affects the effective cleric level needed to use Channel Energy?