if ( $six eq '' ) {  # don't insert }
else { # ok to insert }

# or perhaps 
if ( length($six) == 0 ) { # don't insert }
else { # ok to insert }

##</code><code>##

INSERT INTO Customer_Information 
  (CustomerNumber, Name, Address1, Address2, City, 
   State, ZipCode, Email, DefaultPassword) 
VALUES (
   SELECT one, two, three, four, six, 
          seven, eight, nine , sixteen 
   FROM  info
   WHERE six is not null
   )