筆 and 鉛筆: writing with brushes and pencils
Distinguish tool choices, tool conditions, and the order of preparation and use.
Writing with a brush
筆, read ふで, means brush. 筆で大きな字を書きました。 means writing large characters with a brush. 大きな modifies the characters, not the brush.
筆を水で洗いました。 means washing a brush with water. を and で distinguish what was washed from the means used.
Writing with a pencil
鉛筆, read えんぴつ, means pencil. 鉛筆で名前を書いてください。 asks someone to write their name in pencil.
鉛筆の芯が折れました。 says that the pencil lead broke. Do not add that the whole pencil snapped in two.
Preparing and then using
鉛筆を削ってから、絵を描きました。 says that someone sharpened a pencil and then drew a picture. Preserve the order of preparation and use.
筆ではなく鉛筆を使いました。 means using a pencil rather than a brush. The negative concerns the choice of brush, not tool use itself.
What is described as large in 筆で大きな字を書きました?
Show the answer and why
The characters. 大きな modifies 字, not the size of the brush.