Show that (2,3)-satisfability is np-complete
1-in-3-SAT is NP Complete: given a set of clauses, find a value assignment such that exactly 1 literal in each clause is made true (http://cs.nyu.edu/courses/fall14/CSCI-UA.0310-001/1in3sat.pdf).

Reduction from 1-in-3-SAT: negate every literal in every clause of the 1-in-3-sat instance. Now exactly two literals need to be made true in each clause instead of one to have an equivalent solution set. This is your (2,3)-satisfiabililty instance. We don't even need the clauses with two literals.

Example

1-in-3-SAT instance: (a,-b,c), (a, b, -c), (d, e, f)
equivalent (2,3)-satisfiability instance: (-a,b,-c), (-a, -b, c), (-d, -e, -f)