Collectibles are found when delivering products. They drop
randomly from time to time, whether they are from your own displays or
found at your neighbors' fashion houses.
The key word here is randomly: there is no way to know which collectible will fall from a delivery, or if any collectible will fall at all. However, it is important to note that ALL products of a certain style have an EQUAL chance of dropping any item, regardless of duration or type.
This means that in order to obtain, for example, Peace Signs, you can theoretically display all 1-minute Ripped Hippie Jeans of Boho Style, only, until you get them. In this way, you might be able to complete the quest faster, but you'll have to pay attention to items more carefully as they have a shorter display duration and can get dirty faster.
It is important to note that items with a longer display duration have a higher probability of dropping collectibles, however.
Don't forget that while you are waiting for your products to deliver, you can visit neighbors to find products of that style and deliver them for a chance to find the items you need. You can do this an infinite amount of times, provided that your neighbors' orders continue to need boosting.
In this case, to obtain Peace Signs, one strategy could be to deliver 1-hour Boho Style clothes together with friends, and boost each other's orders. If repeated, it shouldn't take long to get all the items you need.