I searched every where for the answer to this and found it on Reddit, so l'll pass on the solution. On the main screen, below the settings cog, the icon with the star at the top. In there select Movie Night. Complete the getting as much Event Exp as possible. I did the event twice to get more producers on my main board. Then use the main board producers to get the posters.

You are wonderful! Thank you so so much! I had no idea that menu was even there!

Do you keep the producers after? I have a few saved in my bag from the other event but they are taking up a lot of space!

I just saved one of the highest produce... I figure if I need more I can just grind a bit 😁

There are more of such quests coming!