Option $2$:

Start with $(p^{{?}^{?}}q)$ as a premise.

Use axiom T to remove the $$ to get $p^{{?}^{?}}q.$

Open a dashed box and use ${?}^{{?}^{?}}$ elimination twice to obtain the separate atomic formulas.

Use axiom $4$ twice, i$.$e$.$ once on each atomic formula, to add a $$ to each.

$,$ Close the dashed box and use $$ introduction twice, i$.$e$.$ once on $p$ and once on $q,$ to get

$$ p and $q.$

Combine $p$ and $q$ using ${?}^{{?}^{?}}$ introduction.

Option $3$:

$,$ Start with $(p^{{?}^{?}}q)$ as a premise.

Open a dashed box and use $$ elimination to get $p^{{?}^{?}}q.$

Use ${?}^{{?}^{?}}$ elimination twice to obtain the separate atomic formulas.

$,$ Close the dashed box and use $$ introduction twice, i$.$e$.$ once on each atomic formula.

Use axiom $4$ twice, once on $p$ and once on $q,$ to get $p$ and $q.$

Combine $p$ and $q$ using ${?}^{{?}^{?}}$ introduction.

Option $4$:

Open a solid box and start with $(p^{{?}^{?}}q)$ as an assumption.

Open a dashed box and use $$ elimination to get $p^{{?}^{?}}q.$

Use ${?}^{{?}^{?}}$ elimination twice to obtain the separate atomic formulas.

Use axiom $4$ twice, i$.$e$.$ once on each atomic formula, to add a $$ to each.

$,$ Close the dashed box and use $$ introduction twice, i$.$e$.$ once on $p$ and once on $q,$ to get

$p$ and $q.$

Close the solid box to get the result.