Hey
I'm 19 yr old female and weigh 51kg but I'm really short, I'm a healthy size I just want to lose the fat in my arms and thighs, I eat mostly healthy, and walk a couple of kilometers a week
I also work out in the gym 2 times a week for about 20-30 minutes I'm pretty tonned everywhere else but nothing seems to be working for my arms and legs!
How can I lose the fat

I would say increase your walking to at lease 3-4 km 4 times a week. Also, look into Pilates. I bought some Winsor Pilates tapes that you can do at home. No machinery is required, just an exercise mat. It is great for toning arms and legs, and building core strength. An added benefit is the peace of mind you feel when you are done.

Pilates is good for working out arms and legs. You can buy videos or look at some on YouTube.