Using the effective field theory with correlations, we study mixed spin−3/2 and spin−1/2 Ising models with random bonds and crystal-field interactions on the honeycomb lattice. The nearest-neighbour couplings Jij are taken as random variables with distribution P(Jij) = pδ(Jij − J)+(1 − p)δ(Jij − αJ), where J > 0 and |α| ≤ 1. In a certain range of negative values of α, the phase diagrams exhibit re-entrant behaviour. In detail, we investigate separately two kinds of disorder: Bond dilution (α = 0) and random ±J interactions (α = −1). In both cases, the influence of the an-isotropy on the phase diagrams shows some new outstanding features.