I estimate 6.8mi as about 11km. That is definitely doable for a novice, though it may not be as fast as Google's estimate at first. Unless there aren't any traffic lights or stop signs, you should figure your overall average speed at no more than 15km/h initially, so budget 45-50min your first time out. (Google is notorious around here for not allowing enough time for stop lights in their time estimates, and that's without having to get back up to speed.)
Of course once you've been doing it for a month you'll definitely start bringing that time down.
If you're asking in this forum, you have to expect we're always going to recommend that
you bike! :) That said, there are places/roads that even I don't feel comfortable cycling regularly. I can use them occasionally, but wouldn't want to ride them every morning and every night. You'll want to check out the route so you know you'll feel safe (or have a bail-out option) even if it's a busy rush hour, or you get caught in a sudden rain, etc.
I would recommend taking a weekend morning and doing a test-ride to work, stop and have a coffee, then ride home. Take at least a half hour break, unless you're feeling really good. You can get a decent estimate of how long the ride will take. Plus it's the weekend, so if you're slower on the return it's not a problem and it'll definitely give you confidence to do the ride on a regular workday.
Cycling to work is one of the best things about my current job; the exercise in the morning - especially on a sunny day - really helps me arrive at work in a good mood, energized and alert. And the ride home literally helps burn off the stress of the day.