What is the ruling on saying: "I rely on you" in matters such as explaining a lesson or preparing lunch?

There is no harm in saying, "I rely on you," if what is meant is an apparent reliance on means, not a heartfelt reliance. The former is permissible, while the latter is a blemish upon Tawhid (monotheism). Means neither harm nor benefit except by Allah's permission, and abandoning them indicates a deficiency in intellect, while heartfelt reliance on them is Shirk (polytheism). Jurists have explicitly stated the permissibility of [the phrase] "I relied on you" in the sense of assigning responsibility. However, "I have put my trust in Allah and then in you" is not permissible, because tawakkul (trust) is a heartfelt act specific to Allah. It is better to close this door to protect Tawhid.