Hola Ashlyn

This "tan" is emphatic and a quantifier, meaning "so" as in for example: "this is so good!" but we didn't include it in the English translation because it sounds odd to literally say "This so special day.." but we included a note as a hint in the exercise that you may have missed while doing it. 

As for "el día siguiente" or "el siguiente día", the tendency in Spanish is to place the adjectives after the noun, not before, therefore you will mostly hear and see "el día siguiente" to say "the following day" - however, with similar phrases, for example, to say "next Monday", it's more common to do the opposite: "el próximo lunes".

Saludos cordiales

Inma