The right translation of the sentence "Do you know that I know Ecuador?" is:
<u><em>¿Sabes que yo conozco Ecuador?</em></u>
Explanation:
The difference between the verbs <em>"conocer"</em> and <em>"saber"</em> is below:
<em>Conocer:</em> It is a verb that is used regularly to mention that people and places are known.
<em>Saber:</em> It is a verb that is used to mention that a person has knowledge or ability that is based on school or autonomous learning (books) or experience with people who have such knowledge.
As you can see in the sentence, in the first part <u>it is mentioned if a person has the knowledge, with respect to what another knows</u>, therefore, the verb that is used is <em>"saber,"</em> in the second part <u>it is mentioned that this person knows Ecuador, and since it is a place</u>, the verb <em>"conocer"</em> is used without a doubt, therefore, the option chosen is: <u><em>¿sabes que yo conozco Ecuador?</em></u>
