Hello, I would like to know how to get Google Search to display my website results when searched similar to the image shown (so as I also get the texts shown in the red-bordered box below)

gsearch

They're called Sitelinks...

Google decides which of your URLs are eligible, and when they show.

It's not possible to specify links should appear, AFAIK. However, if you wish to prevent certain links from appearing, Google Webmaster Tools will enable you to this.

you can manage your sitelinks by interlinking of pages, proper content and backlinks for homepage!

thanks for the tips LaxLoafer and maggykurt

You can enable it from your google webmaster accounts in sitelinks section. there is one option regarding demoting your required links from there you can enable the required function for your website.

Hope this helps.

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