You can definitely work out twice a day, generally speaking. If you're talking about light-to-moderate aerobic sessions and split resistance training, you shouldn't have much to worry about.
I'm assuming that you're not focused on any sport-specific performance training, or worried about fine tuning gains for an upcoming bodybuilding competition. If you're just a dude looking to get/stay fit, your main concern with two-a-days should be avoiding fatigue.
Again, it doesn't sound like you're at risk with the type of programming you noted, but there are multiple ways to monitor your central nervous system (CNS) to make sure aren't taxing it too heavily:
Heart Rate monitor: Take your resting HR every morning. If it's 6-10 BPM more than average, you might not want to go too intense; any more than that, and you may want to consider an active (or inactive) recovery day.
Heart Rate Variability: One of the most accurate methods to conduct DIY CNS testing, but I haven't found a way to do it accurately without a monitoring device, like OmegaWave or NatureBeat.
Grip Testing: Use a dynamometer to check your grip strength. If you're ~5 lbs weaker than your average baseline, you may be approaching fatigue, and should ease up that day.
CNS Tap Test: I recently downloaded a version of this old school test on my Android. I haven't had it long enough to establish a real baseline, but similar to the other methods; if you score significantly lower that day, chill a little bit.
General body awareness: Listen to your body and be honest with what it's telling you.