Learn Spanish (Latin America): No creo que el joven relojero trabaje con tanta precisión. - I don't think the young watchmaker works with so much precision.

You could, but Spanish speakers generally prefer using con plus a noun (like con precisión) over adverbs ending in -mente. This is especially true when adding intensifiers like tanta (so much) or when you want to avoid clunky strings of -mente words in a coordinated series.

Why is trabaje in the subjunctive here?

The phrase no creo que (I don't think that) expresses doubt or a negated belief. In Spanish, this always triggers the subjunctive mood for the verb that follows, which is why we use trabaje instead of the indicative trabaja. If the sentence were affirmative (creo que...), you would use the indicative.

Why is it el joven relojero instead of el relojero joven?

Placing joven before the noun gives it a slightly more descriptive feel, emphasizing his youth as a defining trait in this context. If you put it after (el relojero joven), it sounds more objective, simply distinguishing him from an older watchmaker. Both are perfectly natural!

Why do we use tanta here instead of tan?