Translation:I believe that I am going to stay here.
French and Spanish have something calleld "reflexive verbs. Apparently quedar means one thing without the reflexive pronouns. https://www.spanishdict.com/guide/reflexive-verbs-and-reflexive-pronouns.
Google lists English reflexive pronouns as: I — myself. you — yourself/yourselves. he — himself. she — herself. one — oneself. it — itself. we — ourselves. they — themselves. Here are the Spanish reflexive pronounds that do NOT replace the subject pronouns (which are often optional.) me te se (singular third person) nos (first person plural) vosotros form is OS se (plural third) They change some verbs. we use them also in english. I wash myself. I get myself up. you was yourself. You encourage yourself. etc. some spanish verbs I think change in meaning with the reflexive pronoun. You can make verbs reflexive that are not usually reflexive (get the list) by adding endings. See [https://www.spanishdict.com/guide/reflexive-verbs-and-reflexive-pronouns] that gives these examples. verse verse: to see one’s self hablarse: to talk to one’s self escribirse: to write to one’s self comprarse: to buy (something) for one’s self You can add it to a feeling verb to indicate a feeling state such as getting angry, happy, bored. They can be there to add intensity to a verb so it would maybe mean to REALLY do something in tone. There are lists and I hope the link above works.
There is a special case of them in commands discussed on this page.
It is a total surprise to me that you can add the reflexive to verb forms at the end of a conjugated verb. I know the other placement is after a negative in the sentence so between the negative and the verb but I am not sure of other pronoun order. It will just take one good example but I do not have it. Anyone?
me voy = I leave, the meaning of the reflexive irse; Yo voy= I go from ir = to go. However the me in this sentence belongs to the reflexive quedarse = to stay. IR (conjugated) + a + mainVERB in infinitive is a future tense.
Now when quedarse is the mainverb and YO is the subject reflected into the object me, you can put this reflected object just before voy as Duo has it or as a tail to the mainverb:
Creo que voy a quedarme aquí
Yes, "me voy" means "i'm leaving" but
"me voy A" means "i 'm going TO"
Also, The personal pronoun "me" can appear before the conjugated verb or after and attached to the infinitive.
"Creo que voy a quedarme aquí." and Creo que me voy a quedar aquí." are both correct.
Stanl78265 and Gom8z! The relative pronoun que/ thatis often omitted in English, but it is never omitted in Spanish. See: Relative Pronouns - que http://www.studyspanish.com/lessons/relproque.htm
Gom8z! In Duo's sentence you can have that or omit it. According to the above you must have que
I (a foreigner) think (that) you can have "that" or omit it. My belief is supported by the Oxford Dictionary:
«The word that can be omitted in standard English where it introduces a subordinate clause, as in she said (that) she was satisfied. It can also be dropped in a relative ... » from: http://www.oxforddictionaries.com/definition/english/that