Over time, I've realised that certain words you use when referring to time, such as ’今日’, ’明日’ and ’毎朝’ have no need for you to attach the に particle. However, when saying '六時’, you must attach a に.
For example, ’今日、学校に行きません。’ and ’毎日午前六時におきます。’
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FWIW, a general rule of thumb I find useful (it isn't always true, but it is a great deal of the time) is that the use of に in Japanese is actually very similar to the use of "at" or "on" with time expressions in English. That is, if you would be inclined to say "at" or "on" in English, then に is probably correct in Japanese, and for time expressions which we don't usually say "at"/"on" with, Japanese also generally does not use に:
六時にご飯を食べました - "(I) ate dinner at 6 o'clock"
木曜日に本を返します - "(I) will return the book on Thursday"
今日(は)学校に行きませんでした - "(I) did not go to school today" (no at/on)
来週やります - "(I will) do it next week" (no at/on)
It's worth noting, though, that "in" is different from "at"/"on", and time expressions which use "in" in English usually don't use に in Japanese:
8月は天気がいいです - "The weather is nice in August"