Question

Ayer yo (prometer) llevar a mi sobrino al cine.

Answer 1

Ayer yo prometí llevar a mi sobrino al cine.
This sentence means - Yesterday, I promised to take my cousin to the cinema.
When it comes to the word ayer (= yesterday), you know immediately that you should use the preterite form of a verb, which in this case is prometer. For first person singular, I, that form is prometí. 

Answer 2

Prometi (promised). Hope I helped!