Structure
[い]Adjective[い] + く + て
おもしろい + く + て
新しい + く + て
[な]Adjective + で
しずか + で
好き + で
Noun + で
先生 + で
仕事+ で
Exceptions:
 いい→よくて
Details
- Adjective + Conjunctions 
- Particle / Auxiliary Verb 
- Standard 
About Adjective + て・Noun + で
The て form of an い-Adjective, or で form of a noun (or な-Adjective) is exactly the same as the て form of a verb, in that it carries the meaning of 'and', and is used for linking. It will allow us to list multiple qualities/traits of something.
For い-Adjectives, we will need to change the last い to く (the form used for conjugation), and then simply add て.
For nouns and な-Adjectives, we will need to add で to the base form (not な or だ).
It should be noted that て and で are different structures here. て is the same conjunction particle that is used with verbs (meaning that い-Adjectives are similar to verbs), while で is actually a form of だ that is used for conjugation. It is the same で as the one that is used in the formal version of だ, である. Which we will learn later.
Caution
Like other て forms (ている 1, ている 2, and ている 3), the て (or で) form of other words can have several possible meanings. These meanings are as follows.
Linking - Like 'and' in English.
Reasons - Like 'with (A)', or 'because of (A)' in English.
Manner - Like 'to do (B) in an (A) way' in English.
Caution
As with all other conjugations of いい, remember that it will be よくて, and not いくて.
Related
Examples
--:--
- 新しい → 新しくて - New → New and... 
- 大きい → 大きくて - Big → Big and... 
- 嫌い → 嫌いで - Dislike → Dislike and... 
- 静か → 静かで - Quiet → Quiet and... 
- 病気 → 病気で - Disease → Disease and... 
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- Online- て vs. と- Tofugu 
 
- Offline- Tae Kim's Japanese Grammar Guide- Page 103 
- みんなの日本語 I- Page 104 [CH 16] 
 
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Adjective + て・Noun + で – Grammar Discussion
Most Recent Replies (13 in total)
 - IcyIceBear - きらい is な adjective so it should be 嫌いで - It looks like an い adjective and there’s so way to tell it’s not in this case, it’s one you just have to remember. Don’t worry, it’s one of few 
 - OldRosy - Thank you! 
 - cyberjus - Having this earlier in the N5 lessons would have reenforced some of the other points. Like ~てもいい 
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