All the given options are prepositions.
A preposition of position is required to fill the blank so that we can know where his place was and where he stood.
'For' and 'since' are prepositions of time. So, they cannot be used in the blank. So, options b) and d) are incorrect.
'Of' is a preposition used to show possession, belonging, or origin. The possession is already implied by the possessive adjective 'his'. So, filling the blank with 'of' serves no purpose. So, option e) is incorrect.
Now, both 'between' and 'among' are prepositions of position.
'Between' means 'in or into the space that separates two places, people, or objects'.
'Among' is used when more than two things are mentioned.
Now, the sentence mentions he took his place near his father and oldest brother (that means two persons only). So, 'between' will fit in the blank.
Hence, option a) is correct.
Note: Possessive Determiners/Adjectives: Words like 'my', 'our', 'your', 'his', 'her', 'its', and 'their' are known as possessive adjectives (or possessive determiners). They come before nouns and indicate ownership of the noun. Example: "The teacher asked the students to open their drawing books."