Here are some steps to be able to call back a private number:

1. Pick up the phone. You can only call back a private number if you pick up the phone before anyone else calls you.

2. Dial 69. In most states the phone company will allow you to call back a private number by simply dialing 69.

3. Try other codes. The majority of the time 69 will work. However, it depends on your area. If the private caller is from your local area 57 should work. Other codes to try are 71 and 67. These codes are typically universal (the same) for most telephone companies. If all of these codes fail call your local telephone company to get the codes specific to the company you use.

4. Stop private numbers from getting through. Most phone companies offer services such as call block, call rejection, call trap or call screening. In most cases it will cost you an extra $3.95 or more each month. Call your phone service provider to find out what is available in your area. If a person calls from a private number, your phone will require the individual to identify the number before getting through. These services are not always available in rural areas. source