Hello!
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The number of field lines in a given area does NOT depend on how far the region is away from a source charge.
The number of field lines depends SOLELY on the strength of the charge of the source. Therefore, the amount of field lines encompassed by a shell of radius 'R' and radius '2R' is the same.
The ONLY thing that changes as a result of increased distance is the spacing between the electric field lines which signifies the decreasing electric field strength as you move farther away from the source charge.