Beginner looking for extra eyepieces for telescope I have a Bushnell Voyager Reflector telescope. It came with 2 eyepieces: k4mm and k20mm. And I am trying to find additional eyepieces to zoom in further on planets and stars, but the bushnell website doesnt offer any. I am unsure if other brands will work with the telescope. Or is my teleacope not powerful enough to look further out.
First of all, any eyepiece of the correct diameter will work with your telescope. Typical diameters are 1.25" and 2". 

The eyepieces you have listed tell you the focal length of the lens. This relates to the magnification - the focal length of the telescope divided by the focal length of the lens will tell you the magnification. So the 20 mm eyepiece will give you lower magnification than the 4 mm eyepiece. Thus to work out the magnication you will need to know the size and focal length of the telescope for starters. A Google search showed there are at least a couple of models but your owner's manual will give you this information. 

Now a caveat: Forget (at least a bit) about magnification. Many telescope brands will [try to] sell the magnification, because this is a big selling point. BUT higher magnification might just turn a small fuzzy blob into a bigger fuzzy blob. 

The most important features of a telescope are the aperture (diameter) and lens/mirror quality. Bigger aperture means more light means easier to see faint stuff. And a quality lens means the difference between a fuzzy blob and a crystal-clear image. 

You will probably find that the mirrors in your telescope are reasonable quality; the lenses are usually where the sellers save on cost. I am confident that if you buy a good quality lens in the 10-15 mm range and one in the 20-25 mm range you will see very nice, clear images of the Moon, the planets out to Saturn, nebulae and star clusters.