Computing Power Requirement For Solar Setup
On a very basic level you have it correct(or at least a reasonable estimate), but we can get more detailed and in depth.

First of all, 12v * 40 Ah gives 480 Wh NOT watts.  Watt-hours, I.E. 480 watts for 1 hour or 240 watts for 2 hours etc.  A technicality that doesn't change your calculations, but might make future calculations less confusing. 

Your first assumption about lead acid batteries and not discharging more than 50-60% is, in general, a correct assumption. However, you call it a deep cycle battery, and a good quality deep cycle lead acid battery may tolerate up to 80% depth of discharge.  Less discharge is always better, but the better deep cycle batteries do allow a lower discharge and still have a reasonable cycle life.  The only way to know is to look at the data sheet from the manufacturer.

Your second assumption is that your battery will simply charge in a linear fashion.  Although your calculations for how long it will take to charge your battery are an OK estimate, in reality a lead acid battery charges to 70% in 5-7 hours (if your solar panel can provide enough current) and the remaining 30% in the following 7-10 hours.  Lead acid batteries follow a 3 stage charge algorithm (maybe 4 stages depending on your charge controller). 

So in your battery if you discharged it 75% = 10a remaining. To get up to 70% need 18a (10+18=28a). 18A÷5h=3.6a/h which your panel is capable of and you said you have at least 6 hours of sunlight and it will take 5 hours to 70% so in the last hour the battery will continue to charge past 70%.  So if you only have 6 hours of sunlight and your controller strictly follows the 5 hours to charge to 70% algorithm,  then you will not fully charge the battery each day IF you discharge to 75%!  In all likelihood your charge controller will take advantage of your panel's ability to provide more than the 3.6 amps and charge the battery a little quicker, but not much - there are limits.

Finally your router.  Does it use AC power?  If so, then you need an inverter which will convert the battery power to 120 volt AC which you will plug in your router.  All inverters are somewhat inefficient and you will lose at least 15% of your solar power to the inverter.  So add this to your calculation and you will find out how long your router will be powered.