am I entitled to know the details of charges an attorney bills me? Example: made a phone call, how long, to who, and what was charge for that incident

If this is your attorney, its certainly a reasonable request.  If this charge for an opposing party's attorney and is something you are being asked to pay as part of a contractual provision of some kind, you can certainly ask for details but I suspect you won't get a substantive response because the attorney will say that to do so would require releaving confidential information protected by the attorney client privilege.  But there's no harm in asking.  You could have another attorney review it and see if the time billed appears to be too much for the likely services.  For example if the charge was for preparing a letter enclosing a copy of a pleadiing of some kind and the charge was for one hour, that would look fishy to me.