Ohayogosaimasu 

I'm not understanding what the “de” means in “wa suki de wa arimasen”. Arigato

I can't speak to what its actual purpose is, but here dewa arimasen 「ではありません」is just the more formal version of ja arimasen「じゃありません」.  You need to use one or the other.  

You'll also see the less formal (but still polite) janai desu「じゃないです」, and the casual janai「じゃない」.

Arigato! So, dewa arimasen and ja arimasen are equivilant but used in different social heirarchical situations. Very helpful.

Yeah. I think dewa here seems super formal, I think in regular polite conversation people are more likely to say ja arimasen or even more likely janai desu. This last form is the easiest for people because it's just taking the casual form they'd use at home and adding desu to keep it in polite language. I suppose in Japanese culture they have a very keen sense of when to use each of these (depending on the situation and who they are speaking with).

Very helpful! Arigato!

こんにちは (Konnichiwa) Heru-,

Thank you for your question! 

The で (de) in 好きではありません (Suki de wa arimasen) “(I) do not like it” is part of the structure used to make negatives in Japanese. (It doesn't have a translatable meaning, as such!)

EarleyGrave has the perfect explanation for this one: ではありません (de wa arimasen) is the more formal version of じゃありません (ja arimasen) and じゃないです (janai desu)! 

These three all mean “not” and are used after nouns and な (na) adjectives to make them negative; however, they all have slightly different levels of fomality:

ではありません (De wa arimasen) is the most formal and is used most commonly in written Japanese. You'll see this used in official contexts like in the newspaper or a textbook. 

E.g. 好きではありません。 (Suki de wa arimasen.) “(I) do not like it.”

じゃありません (Ja arimasen) is still very formal; however, since じゃ (ja) is a contraction of では (de wa) it is less formal than ではありません (de wa arimasen). You will see this used in formal speech in official contexts, such as on the news or in a speech. You might also use it when talking to your boss or a customer to make sure you are speaking very politely. 

E.g. 好きじゃありません。 (Suki ja arimasen.) “(I) do not like it.”

じゃないです (Janai desu) is the least formal way of saying “not”; however, it's not impolite, since it has a polite です (desu). じゃ (Ja) is the contracted version of では (de wa) and ない (nai) is the casual version of ありません (arimasen). じゃないです (Janai desu) is most commonly used in everyday polite speech, such as when talking to neighbours, work colleagues, or strangers. 

E.g. 好きじゃないです。 (Suki janai desu.) “(I) do not like it.”

Japanese has one more way of saying “not”: じゃない (janai). Since this doesn't have a polite です (desu), it is casual, and should ONLY be used whent talking to close friends, family, or children. 

E.g. 好きじゃない。 (Suki janai.) “(I) do not like it.”

I hope this helped!

勉強を頑張ってください！ (Benkyō o ganbatte kudasai!)