For "Capable"
* "Able" is the most common substitute for "capable" in the 3rd person. For example: "She is able to lift heavy weights."
* "Allowed" could be used if you're referring to permission: "He is allowed to enter the building."
* "Authorized" is more formal than "allowed" and implies official permission: "They are authorized to access the database."
For "Permit"
* "Allow" is the most direct substitute for "permit" in the 3rd person: "The rules allow visitors to stay for two hours."
* "Authorize" could be used to imply official permission: "The government authorizes the import of certain goods."
Other Possibilities
* "Enable" could be used to describe making someone capable of doing something: "The new software enables them to work remotely."
* "Empower" could be used to describe giving someone the authority to do something: "The manager empowers her team to make decisions."
Examples:
* "He is able to solve complex problems."
* "The company allows employees to work from home."
* "The teacher authorized the student to leave early."
Remember to choose the word that best reflects the meaning you want to convey.