If you name the thing that is seen in the sentence, then this thing must appear in accusative case, because the verb sehen wants it's object to be in this case. Btu you also can omit this part. Then you say only, that the subjects sees something, but you just don't say what it is:
But in your sentence not a thing, but an action is seen. If the action can be described with a noun, you can use the same construction as before:
Sie sehen den Einschaltvorgang.
You see the power-up process.
But you also can put the action in a dependent clause that begins with the conjunction »wie« and is separated from the main clause by a comma. This is only possible if the verb is a verb of perception (sehen, hören, fühlen, schmecken, ...)
Sie sehen, wie man das Gerät einschaltet.
You see how to turn on the device.
The grammar inside this dependent clause is completely independent from what's going on outside of it. This means, that there is no influence from outside that enforces accusative case inside the clause. The reason why das Gerät still is in accusative case is inside the clause: It's the verb einschalten that enforces das Gerät to be in this case. Other verbs would enforce other cases:
- dative (entkommen needs a dative object)
Sie sehen, wie man der Gefahr entkommt.
You see how to escape the danger.
- genitive (gedenken needs a genitive object)
Sie sehen, wie die Gemeinde der Toten gedenkt.
You see how the community remembers the dead.
What was said before, was all about what was seen. But you add another part of speech that is optional in every sentence: An »adverbiale Bestimmung« (adverbial phrase):
- Sie sehen den Saturn durch dieses Fernrohr.
You see Saturn through this telescope.
- Sie sehen den Saturn mit seinen Monden.
You see Saturn with its moons.
- Sie sehen den Saturn während der Mittagspause.
You see Saturn during the lunch break.
An adverbial phrase looks like an prepositional object but is not an object. An object is ruled by the verb, but adverbial phrases are not. You can add and remove them and still have a correct German sentence. And you can add adverbial phrases with almost any preposition and as many as you want.
But the point is: an adverbial phrase (and also a prepositional object) consist always of a preposition and an inner object, and the case of this inner object depends only on the preposition, not on anything else, so it doesn't depend on the verb.
You see 3 examples above and they use three different cases for the inner object of the adverbial phrase:
- »durch« needs accusative case
- »mit« needs dative case
- »während« needs genitive case
These are three examples for prepositions that need always the same case. But German also has prepositions that use accusative cases for directions and targets of movement and dative case for places. They are called »Wechselpräposition«, and »in« is one of them:
- Anna geht in dem Haus.
Anna walks inside the house.
- Anna geht in das Haus.
Anna walks into the house.
In #1 the inner object »dem Haus« is in dative case, so it describes a place where the walk happens: inside the house
In #2 the inner object »das Haus« is in accusative case, so it describes a movement towards a target: into the house
In your sentence you don't see something into the depiction. This wouldn't make any sense; you can not move anything just by seeing it. But you see something inside the depiction. And that's the reason why you need dative case after in:
Hier in der Abbildung sehen Sie, wie man das Gerät einschaltet.
- The part »in der Abbildung« is an optional adverbial phrase (adverbiale Bestimmung) that is grammatically independent from the verb.
- The preposition in allows dative and accusative case.
- There is no movement into something, but an action that happens inside something, so it must be dative case.