No,a twelve mile round trip 4 days per week is not too far. It's flat, even a new cyclist will be able to maintain a comfortable 12mph, that's only a half-hour each way, you'll be fine. If you are very out of shape and find it tiring, start with two or three days per week and build on that.

Don't be discouraged under any circumstances. Choosing to commute by bike will be the best decision you have made in a while. And within about three months you'll get faster, your journey time will fall and you'll be looking for ways to spend more time on the bike.