It depends on many factors, some info here:

http://ecmweb.com/code-basics/box-fill-calculations

Assuming 12/2, no internal clamps (looks like they're on the outside), no devices in the box....

2+3 12-2's would be 10 conductors
the grounds would be 1 condcutor.

12g uses 2.25 cu in per conductor, so you need 24.75 cui inches. A 4" box is typically a touch over 30 cu in (it should be marked on the box), You'd be OK.

4" boxes are available in varying depths. The depth must be included when calculating the volume of the box. Boxes with similar appearance and shape are available in 4 11/16 square. The 4 11/16 are highly unlikely to have non-metallic cable clamps but can be used with cable connectors.

I was basing my estimation of the boxes in his picture which looks like the 30.30 cu in boxes and he's got external romex clamps and knockouts of the sort that doesn't look like there are internal clamps on those boxes.