precision m 6700 RAM upgrade

Yes, it's a dual core CPU, with maximum four threads.

You can use 16 GB RAM. Crucial shows some compatible RAM here. 

You needn't buy a big brand name such as Crucial. I recently bought a relatively unknown brand, Kuesuny, through Amazon for much less than the price of a big brand name, and I'm happy with it. I ran memory tests for a couple of days to thoroughly test the RAM when I first installed it. It performs well and saved me money.

Ideally, you should install a matched pair of two identical 8 GB sticks, for a total of 16 GB. If your system currently has a single 8 GB stick, you could try to add another 8 GB stick with the same speed and timings, and it may work.

However, it's likely that your laptop currently has two 4 GB sticks, so you'd need to remove both to install two 8 GB sticks to achieve 16 GB. You can check what you currently have via a variety of methods, including in Task Manager.

That laptop is ten years old. It may be crashing due to heat. The thermal compound has dried out and cannot adequately transfer heat away from the processor, and there may be a lot of dust inside the laptop and maybe inside the fan and heat fins. So, your laptop is unable to adequately cool itself.

You might consider an internal cleaning. Open it up to clean out dust. Disassemble the fan to clean out dust and fluff. I found a fair bit in two laptops I worked on recently. Remove the heat sink, remove the old thermal compound and apply new thermal compound before reinstalling the heat sink.

While you're in there, replace the CMOS battery. If it isn't dead, it soon will be. BIOS settings and date/time can't be saved without a functioning CMOS battery.

Before opening the laptop, rest it on an anti-static mat or at least a reasonable alternative such as corrugated cardboard. Wear a grounded wrist strap, also called anti-static wrist strap, ESD wrist strap, or ground bracelet. I know many people do such work without this, but it's a cheap and sensible precaution.