Translation:How are you?
שלומך comes from the word Shalom, which means "Peace" so you can say that you are asking "What/how is your peace?" (the YOUR is what gives it the ending ך) where in reality it's more "How are you doing?"
If you pay close attention to the word שלומך you wil see a kamts sign in the last letter . it makes the sound of the ך kha which is adressed to a male and read shlomkha. If you se a shva sign (looks like a small : ) it will adress a female, making the sound of kh and read shlomekh HTH
I think "how are you" is closer to how this phrase is used. It is the most formal way to say it in Hebrew.