Front V-brake not working
The 'noodle' (the curved silver tube the brake cable passes through) has slipped through  the holder on the right-hand (in your picture) brake caliper. The noodle is designed to come out of the holder to spread the calipers to enable the wheel to be taken out.

The proper configuration looks like this:



Squeeze the calipers together and free the noodle from the holder. Pull the dust boot off the end of the noodle, you should see a little flange on the end - that fits into the end of the holder. Before you attempt to fit the noodle in the holder, slide the cable housing into the other end of the noddle, and also make sure the housing is inserted in the brake lever body on the handlebar. Squeeze the calipers together to fit the end of the noodle in the housing. When the noodle is back in the holder you can push the boot back on.

if that's not clear, here's a video on assembling v-brakes at a point where it shows how the noodle fits in the holder.


                
            

Updates based on futher info:

The flange has come off the end of the noodle. Normally the flange is permanently fixed to the noodle and it should not come off. You can probably shove the flange through the boot with the noodle, then slip it back on the end of the noodle, and re-assemble the brake as in the Park tool video. That will get the brake working. The real solution of course is to get a new noodle. A local bike shop will have one, they can also be found on Amazon or any of the the on-line bike stores.