at least / after all
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at least
Expresses a limitation that softens a negative situation; means something like 'wenigstens' (at least) or 'zumindest' (at least).
Ich habe den Zug verpasst, aber immerhin scheint die Sonne.
I missed the train, but at least the sun is shining.
'Immerhin' (at least/after all) can stand in position 1; then the verb follows immediately. It can also stand in the middle of the sentence after the verb and the subject in order to comment on a statement.
Immerhin hat er sich entschuldigt.
At least he apologized.
In this meaning, a negative or disappointing situation is often described first. 'Immerhin' (at least) then introduces a positive aspect that makes the situation a little better.
Das Auto ist kaputt, aber immerhin haben wir eine Versicherung.
The car is broken, but at least we have insurance.
In this meaning, 'immerhin' (after all) is used to emphasize a reason or an important circumstance that should not be forgotten. It often expresses slight surprise or a justification.
Du kannst nicht erwarten, dass er perfekt ist. Er ist immerhin noch ein Anfänger.
You can't expect him to be perfect. He is still a beginner, after all.
because
'denn' and 'immerhin' can both justify a statement or make it easier to understand. 'denn' connects two main clauses and directly gives the reason for what was said before. The word order stays the same as in a normal main clause. 'immerhin' is not a conjunction, but an adverb. It emphasizes that a fact is important or surprising, often as an argument for an evaluation. Learners may confuse the words because 'immerhin' sometimes feels similar to 'schließlich' (after all) or 'denn'. In practice: with 'denn' you give a reason; with 'immerhin' you highlight an important point.
Anna ist zufrieden mit dem Ergebnis, immerhin hat sie nur zwei Tage gelernt.
Anna is satisfied with the result; after all, she only studied for two days.
Ich nehme heute den Bus, denn mein Fahrrad ist kaputt.
I'm taking the bus today because my bike is broken.