Which excerpt from the story “Marriage Is a Private Affair” illustrates the tension between the characters best? “That night he hardly slept, from . . . fear he might die . . . .” “[I]t is impossible for me to marry Nweke’s daughter.” “You have lived in Lagos all your life . . . .” “Nnaemeka and his young wife were a most happy couple.”

The excerpt that best illustrates the tension between the characters in the short story is when Nnaemeka tells his father,

"[I]t is impossible for me to marry Nweke’s daughter" (Achebe, 2).

Nnaemeka's comment indicates that he insists on challenging the traditional Igbo marriage customs by choosing his own bride. Nnaemeka's father has already chosen a bride for his son, who Nnaemeka remembers as being an "Amazon of a girl." According to traditional Igbo culture, a man's parents choose his bride and marriage is not based on individual choice or love. Nnaemeka's refusal to marry Ugoye Nweke reveals his love for Nene Atang but ruins his relationship with his austere, traditional father. Nnaemeka's father feels disrespected and takes offense to his son's decision to marry Nene instead of Ugoye Nweke. As a result of Nnaemeka's engagement to Nene, Nnaemeka's father stops talking to him and refuses to acknowledge his son or daughter-in-law. The tension between Nnaemeka's decision and his father's insistence on his son marrying Ugoye demonstrates the conflict between modernity and tradition. Nnaemeka's views regarding marriage are modern while his father's beliefs are traditional.

The excerpt that best illustrates the tension between the characters is “[I]t is impossible for me to marry Nweke’s daughter.”
This excerpt references the tense conversation between Nnaemeka and his father about Nnaemeka's choice of a bride. During the conversation, Nnaemeka tells his father that he cannot marry Jacob Nweke's daughter; he argues that modern marriages are based on love.
However, Nnaemeka's father disagrees. He is adamant that a man should choose a bride based on traditional concepts. He expects Nnaemeka to marry Ugoye Nweke because it has already been decided. When Nnaemeka tells his father that he wishes to marry Nene Atang instead, the latter becomes visibly upset. 
Nnaemeka does his best to convince his father of the rightness of his choice, but his father refuses to listen. Instead, Nnaemeka's father elects not to attend his son's wedding, and he even refuses to meet Nene Atang. Thus, the excerpt "It is impossible for me to marry Nweke's daughter" illustrates the tension between father and son in the story.