I found this ad/sticker in a restaurant, in a Philippine city where a large
number of Japanese students study English.

> 英語が伝わる楽しさをより多くの方へ

I have no idea how to make of this statement.

I understand the individual phrases/words but not why the sentence is formed
as such.

  1. 伝わる楽しさ: is this a common formation (ru verb+ noun)
  2. Is there another way to say this sentence? (In japanese?)
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question
syntax
I don’t understand the structure of 英語が伝わる楽しさをより多くの方へ
１．「英語が伝わる楽しさ」 is a noun phrase, where the relative clause 英語が伝わる (your English
is understood) modifies 楽しさ (joy, pleasure). For "Gapless relative clauses",
please refer to [this post](https://japanese.stackexchange.com/a/14550/9831).

「英語が伝わる楽しさ」 _lit._ joy where/when your English is understood → joy of making
yourself understood in English

「～～楽しさをより多くの方へ」 literally means "joy (of ~~) to more people". The predicate,
or verb phrase (like 届けたい or 届けます perhaps?) is left out as implied. (This kind
of omission is often used as a stylistic device in slogans, ads, lyrics,
song/film titles etc. e.g. 『アルジャーノンに花束を』『まごころを、君に。』)

２． I would rephrase it as...

「英語が伝わる（ことの）楽しさを、もっとたくさんの人たちへ（届けたいです / お届けします）。」  
「英語が伝わる（ことの）楽しさを、もっとたくさんの人に（感じてもらいたいです）。」  
etc...
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answer