Hi,
Microsoft DirectX is included as an integral part in Windows operating systems. You can update DirectX by applying the latest service pack or other updates through Windows Update.
Some applications and games require DirectX 9. However, your computer includes a more recent version of DirectX. If you install and then run an application or game that requires DirectX 9, you might receive an error message such as "The program can't start because d3dx9_35.dll is missing from your computer. Try reinstalling the program to fix this problem."
DirectX 11.1is the default version of DirectX installed on Windows 8.
How to install the latest version of DirectX
http://support.microsoft.com/kb/179113/en-us#
How to check which version of DirectX is installed:
Swipe in from the right edge of the screen, and then tap Search. (If you're using a mouse, point to the upper-right corner of the screen, move the mouse pointer down, and then click Search.) Type dxdiag in the search box, and then tap on click dxdiag.exe.
I would like to inform you that FIFA 2006 is not compatible with Windows 8.1. You can refer to the following link to check the compatibility of Fifa 2006 with Windows 8.1.
You can try to install the game in compatibility mode and check if it helps.
You can follow the link given below to install the game in compatibility mode.
What is program compatibility?
http://windows.microsoft.com/en-US/windows-8/what-program-compatibility
Make older programs compatible with this version of Windows
http://windows.microsoft.com/en-US/windows-8/older-programs-compatible-version-windows
Hope this helps.
Please post back with the status of the issue and we will be glad to assist you further.