Hi Sara,
There are a few things you need to understand first. In order for Intel HAXM to work, you need an Intel (x86) processor which supports virtualization. If you know the model of processor that you have, check the necessary VT-x capability on ark.intel.com (based on the system specs you mentioned, I am close to certain that your processor does support VT-x, but let's be sure by checking the site I gave you). In order to know which model of processor you have, you may wish to use the freeware CPUz (CPUID).
Intel HAXM allows you to virtualize the CPU. The Android emulator channels OpenGL calls to the GPU (in your case, your Radeon HD graphics card). This is done even without Intel HAXM. You can get more infor by checking this blog article: https://software.intel.com/en-us/blogs/2015/07/17/a-quick-peek-at-hardware-accelerated-android-emulation-using-intel-hardware
After you confirm that your processor supports VT-x, make you that VT-x is enabled in the BIOS of your computer. Check the Troubleshoot section from this article for more information.
Let me know what was the outcome after trying the above.
Best regards,
Shailen.
