You cannot control this at your end. This is Google search suggestions, and it is based on the number of searches for particular keyword phrase.
Thank. But sometimes they show the domain name like www.site.com If i want my site on the list, should I type and search my own site on google so that it will appear in the box? one of my competitor site is only 1 month, and his www.site is on search suggestion already
This tools can give you some idea about popular search keywords to optimize; http://www.google.com/sktool/#
That or your keywords are very unique. I noticed a new site I know of that got this honor and they have no traffic at all.
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