Let PD2,3(n) count the number of partitions of n with designated summands in which parts are not multiples of 2 or 3. In this work, we establish congruences modulo powers of 2 and 3 for PD2,3(n). For example, for each \quad n≥0 and α≥0 \quad PD2,3(6⋅4α+2n+5⋅4α+2)≡0(mod24) and $PD_{2, 3}(4\cdot3^{\alpha+3}n+10\cdot3^{\alpha+2})\equiv 0 \pmod{3}.