Learn Spanish (Spain): Me gustaría que hicieras el enigma con nosotros. - I would like you to do the riddle with us.

The main verb gustaría is in the conditional tense (I would like). When you express a wish or desire in the conditional, the following verb in the subordinate clause must match its timeline. This requires using the imperfect subjunctive (hicieras) rather than the present subjunctive.

How do we get the irregular stem for hicieras?

The imperfect subjunctive is always built from the third-person plural (the ellos / ellas form) of the preterite (simple past). For the verb hacer, that form is hicieron. We drop the -on to get the base hicier-, and then add the tú ending -as.

Enigma ends in an -a. Why does it use the masculine article el?

Several Spanish words ending in -ma are actually masculine because they originally come from Greek. You have likely seen this rule before with words like el problema, el idioma, and el sistema.

Could I translate "I would like" as querería instead of me gustaría?

Technically yes, but native Spanish speakers rarely use querería in this context. To politely say "I would like", it is much more natural to use me gustaría (literally "it would please me") or quisiera.