4

For example, a sentence like the following:

You can lose weight by eating more vegetables.

5

Version 1:

Du kannst abnehmen indem du mehr Gemüse isst.
Sie können abnehmen indem Sie mehr Gemüse essen.

Version 2:

Dadurch, dass du mehr Gemüse ist, kannst du abnehmen.
Dadurch, dass Sie mehr Gemüse essen, können Sie abnehmen.

Version 3a:

Durch das Essen von mehr Gemüse kannst du abnehmen.
Durch das Essen von mehr Gemüse können Sie abnehmen.

Version 3b:

Du kannst durch das Essen von mehr Gemüse abnehmen.
Sie können durch das Essen von mehr Gemüse abnehmen.


The subjunction »indem« and the pronomial adverb »dadurch« in combination with the subjunction »dass« both work similar to the English »by« in this construction, but both of them open subordinate clauses which need their own subjects, and so you have to use »du«/»Sie« twice in the versions 1 and 2 (once in the main clause and once in the subordinate clause).

The versions 3a and 3b are the same construction, just in two different word orders. Grammatically they are closer to the English original, but they are a little bit less common than 1 and 2 in German, because here we need to nominalize the verb (i.e. you need to turn the verb »isst/essen« into the noun »das Essen«), wich makes this construction a little bit more awkward than version 1 or 2.

About word order in 3a and 3b:
The part »durch das Essen von mehr Gemüse« is a prepositional object, i.e. one single part of speech. »Du«/»Sie« is the subject. »Können« is the verb, that in German statements always must stand on position 2, and »abnehmen« is an infinitive that always must exist when you use modal verbs like »können«. This infinitive is part of the predicate and must stand on the last position of the sentence.
So, we have four parts of speech, two of them occupy fixed positions (können on position 2, abnehmen on the last position which here is #4), so only the subject and the prepositional object can float around in the sentence freely, which gives the two versions a and b.

(Btw: Note, that your sentence is wrong in content: You can't loos weight by eating more (of whatever). Here is the universal trick for loosing weight: Eat less!)

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