Concept:
The phrase
\[
\text{shall have written}
\]
is future perfect tense.
Future perfect tense is used to show that an action will be completed before a certain time in the future.
The preposition used for completion before a deadline is
\[
by
\]
Step 1: Identify the tense.
\[
\text{I shall have written}
\]
This is future perfect tense.
Step 2: Identify the time expression.
The time expression is
\[
6\text{ pm}
\]
The action will be completed before or at \(6\) pm.
Step 3: Choose correct preposition.
The correct preposition is
\[
by
\]
So the sentence becomes:
\[
\text{I shall have written my exercise by 6 pm.}
\]
Step 4: Final answer.
\[
\boxed{\text{by}}
\]
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