Im doing a school project about improving better rail links to my school's local and I'm wondering if the merseyrail line from Chester to Liverpool will be able to take 6 extra trains an hour
The line from Chester to Birkenhead Central could certainly take extra trains, assuming some money were available to resignal it with reduced headways. Six extra services would take it up to 12tph each way, which is identical to, for example, Cardiff Queen Street to Central. But these services are straight through. If the driver had to change ends and reverse then you'd need to think about extra platforms in which to do so.
The most congested part of the Wirral route is, of course, the loop line, which has got services from West Kirby, New Brighton, and Ellesmere Port in addition to Chester. That's 14tph each way at Hamilton Square, and going around the single track loop. As some people have mentioned above, there are some examples of higher frequencies, but it will require even shorter headways, closer signalling, and also more rolling stock. Adding your extra six services and going to 20tph will mean a train going through the loop every three minutes, and that's approaching city subway frequencies. (At a glance the Bakerloo Line in London apparently barely breaks 20tph in the rush hour.)
You could also consider portion working to increase service frequency to Chester. There are already paths for six trains an hour coming as far south as Hooton, but two go to Ellesmere Port instead of Chester. If you had enough rolling stock, and perhaps some investment in signalling at Hooton, you could split trains there and serve both lines with only one path out of Liverpool. (The trouble with that is that having split you only have three carriages going to Chester. Is that enough for the number of passengers wanting to travel?)
