A rule of thumb: every 50mm of "full-frame (35mm sensor) equivalent focal length" is equal to 1x of magnification. Since the Rebel t4i is a "crop sensor" camera you multiply the lens focal length by 1.6. So, your 300mm lens is a 480mm lens in full frame equivalency.
Then you take this number 480 and divide by 50 to get your magnification. So 480/50 is 9.6x.
Super-zoom bridge cameras give a lot more magnification with still very good image quality. However, a "60x zoom" camera does NOT PROVIDE 60x magnification. Instead the 60x refers to how much longer the focal length is at max zoom than min zoom. So a 60x camera might have a full frame equivalency focal length range of 20-1200mm, where 1200 is 60 times 20, but in magnification terms that 1200mm long end is really 1200/50 = 24x magnfication.
If you really want to get close, you need a quality spotting scope and digiscoping setup, which can provide super long effective focal lengths in the 3500mm+ range.
I carry a high quality point and shoot wherever I go. When I have my good Zeiss scope with me I get some pretty decent shots as far as a mile away or so. When I don't have my good but heavy scope with me, which is most the time when actually hunting versus just scouting, I have found that I can get decent but somewhat limited, pictures thru one side of my binoculars. Here are a couple of examples I took last November, thru my Swarovski 10x42 EL's with my Sony DSC-RX100 in marginal light conditions.