I can't install adobe flash player on my galaxy tab3 why?
There is no more Flash Player for Android and there won't be another. Android is no longer compatible with Flash Player. Playing Flash content is very processor consumptive and it drains your battery, also shortening the life of it. Android (Google) recommends using either "Dolphin" or "Puffin" as your browser if you need to view Flash content with a mobile device running Android. They're both availabe in the GooglePlay store. These browsers use "server side" rendering to reduce the load on your device.
2008 (March) - Apple® releases the first iPhone, using iOS®. Steve Jobs is insistent and adamant that iOS® is NOT compatible with Flash® and NEVER WILL BE. Jobs' reasoning is that playing Flash® content is processor consumptive and it drains batteries, thus shortening the life of them in mobile devices. In six years, that hasn't changed. Not for the iPhone®, iPad® or iPod® Touch™. It never will change and there never will be a Flash Player® for iOS®.
2008 (September) - Google® introduces Android™ to compete with iOS®, for people who don't want to pay what Apple® is asking for an iPhone®. Android®, unlike its Apple® counterpart IS compatible with Flash®.
2012 (June) - Android™ (Google®) announces the end of support for Flash® with Android™ 4.3. Going forward NO Android™ devices will be compatible with Flash®, but older versions on older devices can still be loaded with "legacy" builds still available from Adobe®. Android™ (Google®) cites the same reason Apple® did for the decision to end support for Flash®. Adobe® continues to release security patches to Flash Player® for Android™ until September 2013, announcing the "end of life" for Android™ Flash® September 10.
Android (Google) recommends using either Dolphin (https://play.google.com/store/apps/details?id=mobi.mgeek.TunnyBrowser) or Puffin(https://play.google.com/store/apps/details?id=com.cloudmosa.puffinFree) as your browser to view Flash content.