Construct a pushdown automaton for $\{a^{2n}b^{3n}|n\ge0\}$
Your PDA accepts the language
$$ \{a^{i+j} b^{i+2j} : i,j \geq 0 \}, $$
which is different from the one you are interested in. In fact, you can show that it equals
$$ \{a^kb^\ell : k \leq \ell \leq 2k \}. $$