Not being able to remember or find a previous address is a problem that many overseas voters have--you're not alone! However, your local election official in the United States must have an exact address or a precise description of where you last resided in order to determine your voting district and send you the correct absentee ballot.
To start, we suggest you try searching for the exact street address. Try looking at old hospital and medical records, school/work records, old letters/correspondence, and other documents. Ask your relatives, friends, former employers, schools, doctors, etc. for assistance in checking their records. Examining a city map online is also a good tactic to jog your memory.
If you still can't find the address, but can remember enough to describe the location of your former residence in some detail, then you should try to register using that extra descriptive information. When you are generating your Voter Registration/Ballot Request form, in the section entitled "Last U.S. Residence Address" you should check the box that says, "Use Address Description." Then enter your street address description in the "Address Description" box that appears. Here is a sample description: "South side of Hill Street between Forest and Pine Streets, second house from the corner of Forest, aluminum siding with large entry porch."
Then, in the "Additional Information" section of the online process, you can add further notes. For example, you may wish to state your year of departure from that residence, whether you ever registered to vote in that city/town previously, and other information that may assist your local election official in confirming the fact that you once lived at that address.