Delete a partition in a hard drive

I have an old laptop that has a 20 GB hard drive. I have other computers that I use on regular basis but this is more of the "guest" laptop. It runs ok but here is the problem. The hard drive is partitioned and the C: drive has 6GB while the D: drive has 14 GB. Even though I am running bare bones programs, the 6 GB is basically full and I'm left with 198 MB of space left on the C: drive while the D: drive has nothing on it. The low space is causing the computer to freeze up.

How do I safely delete the partition without affecting the programs on the C: drive? I googled it but read some horror stories and different ways to do it.