I am 20 and i'm worried about my weight i weight 12stone 6 and am 5ft 8, is this a healthy weight to be?

Maybe, maybe not: Healthtap doctors are american physicians, so we talk in pounds and ounces. I'm guessing a stone is 14 pounds, so 12 stone 6 = 174 pounds? That might be ok, depending on whether a person is male, female, has lots of muscle, has little muscle, etc... The question of "healthiness" depends on other conditions (a person with diabetes, heart disease, arthritis, etc... Would do better being lighter).

Hard to say: Using simplistic formulas this is overweight by BMI, in the top15-25% of males and top 15% for females. If you were a heavily muscled weightlifter these numbers would not apply. If you are somewhat average you need to do some work.