で(de) — Context of Action (Location, Means, Condition)

• 図書館で勉強します。

  Toshokan de benkyou shimasu.

  I study at the library.

  図書館 (library) で (location of action) 勉強します (study)

• 箸でご飯を食べます。

  Hashi de gohan o tabemasu.

  I eat rice with chopsticks.

  箸 (chopsticks) で (by means of / tool); ご飯 (rice) を (object)

• 風邪で学校を休みました。

  Kaze de gakkou o yasumimashita.

  I was absent from school because of a cold.

  風邪 (cold) で (reason/cause); 学校 (school) を (place left/absented from)

• ・Location (で vs に): 学校で勉強する (the action happens AT school) vs 学校に行く (movement TO school), 学校にいる (existence at school).
• ・Material: Used when the raw material is still visibly the same (木で作る - made from wood). If the material undergoes an invisible/chemical change, から is used (ワインはブドウから作る).
• ・Scope/Limit: Marks amounts, limits, or groupings: 1000円で買えます (you can buy it for/within 1000 yen); 家族で行きます (we go as a family).

Commonly confused with

The JLPT rarely asks whether you recognise a pattern — it asks which of several similar patterns fits. These are the ones で is tested against.

• は (wa) — Topic & Contrast Particle
• が (ga) — Subject Marker & Exhaustive Listing
• を (o) — Direct Object & Traversal
• に (ni) — Target, Time, and Existence Location
• と (to) — And (Exhaustive), With, and Quotation
• か (ka) — Question, Or, and Uncertain Identity
• の (no) — Possession, Modification, & Nominalization
• も (mo) — Also, Too, Both/And, Emphasized Quantity