Umm... I think you should maintain a database of 'suggests' for showing them in the 2nd TextBox
As @bhi said, enable the autopostback property for the 1st textbox and do this-
"Select * from <table> where <field> like" & me.textbox1.text & "%"
This sql is for the 'suggests'. If you need some other field, just modify your sql statement.
Bind the result of this query to your multi-line 2nd textbox.
You can do this in AJAX too.