1. **State the problem:** Factor the expression $2mx - 3m + 2pcx - 3pc$ by grouping. 2. **Group terms:** Group the terms to factor common factors: $$ (2mx - 3m) + (2pcx - 3pc) $$ 3. **Factor out common factors from each group:** From the first group, factor out $m$: $$ m(2x - 3) $$ From the second group, factor out $pc$: $$ pc(2x - 3) $$ 4. **Factor out the common binomial factor:** Both groups contain the factor $(2x - 3)$, so factor it out: $$ (2x - 3)(m + pc) $$ 5. **Final answer:** $$ \boxed{(2x - 3)(m + pc)} $$ This is the fully factored form by grouping.