Garantizo comes from the verb garantizar and means "I guarantee". This word is especially interesting because it sounds quite formal, almost like something you'd hear in a business contract, not a romantic song.
When Prince Royce sings "te garantizo mi amor", he's elevating his promise. He's not just saying he loves her; he's declaring his love is a sure thing, an unbreakable commitment you can count on, especially when others are trying to cast doubt on their relationship.
Prince Royce is shutting out the noise in "Tu Y Yo", setting up an "us against the world" bubble where outside opinions aren't welcome. The whole premise kicks off because the girl's friends are busy badmouthing him, warning her that he is no good and claiming he is out running around: "They tell you that I might be going around cheating / Don't believe them girl they're just hating." Royce shuts down the drama with the Spanish phrase "Te meten cosas en la mente" [They put things in your head / They mess with your mind], which is a classic everyday idiom for someone poisoning your thoughts with gossip. For him, a relationship is strictly business for two: "Lo que sucede es entre tú y yo / Es un problema de dos" [What happens is between you and me / It is a problem of two]. He is telling her to ignore the chatter and remember the baseline fact that they belong together.
To prove his loyalty, Royce pulls out the ultimate sweet nostalgia card: schoolyard romance. He takes her back to day one, reminding her: "En la escuela yo te conocí / Yo te cantaba desde el corazón" [I met you in school / I sang to you from the heart]. He gathered all his courage to confess his feelings back then, and he argues that a bond built on childhood promises shouldn't fall apart over rumors now. He even throws in some dramatic devotion, swearing "por ti soy capaz de morir" [for you I am capable of dying]. It is an intense, protective bilingual plea where he reminds his partner of their history and begs everybody else to simply butt out.