"They themselves search for fourteen horses for tomorrow."
Translation:Ele însele caută paisprezece cai pentru mâine.
In a way it's a bit like how in English we use "own" to reinforce possessive pronouns: "He drives his car" -> "He drives his own car". It's not equivalent though since it's used for different things, but they both do a similar kind of reinforcement so it might be helpful for anyone struggling with this point.
Generally, a căuta is not accompanied by a preposition. Unlike English, in Romanian you search the keys, you search the book (not FOR the keys, not FOR the book). Example, cauți cheile sau cauți cartea). The exception to this is when you are forced to use the preposition pe as an accusative object marker for identified living persons (Tom, my sister, my professor Sam, etc) or living animated objects that you are treating as a living identifiable person (my cat, my teddy bear, etc). So, you can search FOR Tom (cauți pe Tom). But, the use of pe here is not due to the fact that pe goes with the verb a căuta -- in fact, pe normally does not follow the verb a căuta. The only reason the preposition pe would follow a căuta has nothing to do with the verb a căuta, but instead is related to the fact that the preposition pe must be used to mark accusative objects when those accusative objects are identifiable living objects. Naturally, you can treat some objects as identifiable living things or objects (a random dog or teddy bear for example versus my dog Scruffy or my teddy bear that I am imagining is a living person with my childish imagination - depends on the speakers point of view). So, you would say, Văd o carte BUT Văd pe Tom. Lovesc masa BUT lovesc pe Mary. Văd câinele (assuming you are considering the dog to be an object) but vâd pe câinele meu (you are considering the dog to be a person or a living animated object). Are sens?
DornenEngel, you can also take a look here: www.seelrc.org:8080/grammar/pdf/stand_alone_romanian.pdf , see 188.8.131.52.1 pg.34
Sure it does. You just have to squint a little bit. I suspect you will agree that the following sentence makes sense: "They search for fourteen horses for tomorrow." The only difference between that sentence and this Duolingo sentence is the addition of another pronoun of emphasis "themselves." As with many other examples in this section that focus on emphasis pronouns, it is merely emphasizing who did the action (in this case, that the action was performed by the subject, "they").
Here's another example: The President storms into a meeting and demands to know who is responsible for this CDC testing nightmare. His subordinates look up at him sheepishly and answer, "Why, you yourself are responsible for this mess. You don't remember slashing the CDC's budget in recent years because you preferred to reallocate that money to tax cuts for the rich?" <-- Totally fictional example, not intended to bear any resemblance whatsoever to any actual persons or actual events.
The "you yourself" is intended to convey that it was "YOU" and NOT ANYONE ELSE. Cheers.