Hardware Direct X 9 c free download and how it would install main hardware

You need some clarification on how those terms work... In few words, Direct X is a software solution (API is the correct technical term) that binds hardware with it (specifically, graphic processors), so saying you have "Direct X 8.1 hardware" can be directly translated to "I have a video card from the late 2000" (GF4 4x00ti, Radeon 8500). Now, if you actually mean "I have Direct X 8.1 installed on my computer" doesn't say anything about the hardware you have.

This url: DirectX has the installer for the latest one. If you actually have a card from the late 2000, this upgrade will give you compatibility with the software side of things in new games, but if certain games require hardware features your card doesn't have, you won't be able to play them still.

TL;DR: Click on the link to get the latest version of Direct X, but it doesn't guarantee you'll be able to play the latest games if your hardware is way too old.

Cheers!

EDIT: typos
 
You need to be more clear. Exactly what video card do you have and what operating system are you using?

If you have a very old card like the Radeon 9500 from 2003 or lower (8xxx, 7xxx series), or the nVidia GeForce 4xxx series (also from 2003) or before, then you cannot "upgrade" to DirectX 9c simply by downloading software.

DirectX 9 requires specific hardware and you will need at least a Radeon 9600 or GeForce FX 5200 to have that hardware.