How to upgrade my iOS 9.3.5 to iOS 10?

You clearly have an iPad2, iPad3 or original iPad mini. These devices cannot be updated beyond iOS 9.3.5 (WiFi Only models) or iOS 9.3.6 (WiFi & Cellular).

Apple ended update support for these devices in September 2016. None of these models can be updated to iOS 10 or later versions, as the internal hardware does not meet the minimum technical requirements for new versions of iOS/iPadOS. The 32-bit operating system, upon which they are based, is also effectively obsolete.

Many App Developers have also dropped support for older devices and iOS versions preceding iOS11/12/13 - and have withdrawn older versions of their Apps from the Apple App Store, now limiting utility and usefulness of older devices. 

If Apps that you need to use now have higher minimum iOS-version requirements, your only option is to replace your iPad with newer model. Of current models, even the entry-level iPad7 model supports current iPadOS 13.x - and has hardware specifications and capabilities that will vastly outperform your old iPad. Other models provide a corresponding step-up in performance, features and cost.

I hope this information is helpful - if only in clearly stating both the limitations of your existing iPad and your current options.

See the Apple Support article(s) below.

IOS 10 is compatible with these devices

You can't upgrade an iPad 2 any further than where it is now.

Go to settings > About > Software update and click download.

I hope it helps.