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Does it say in the bible that fathers shall have to answer for their children? Where?
The answer I give would depend on what you mean by “answer for” their children. The answer is different depending on if you mean: receive punishment for their children’s sins; be held accountable for how they raised their children; or be held liable for their children’s actions while their children are still under their control.
Ezekiel 18:20 says, “The soul that sinneth, it shall die. The son shall not bear the iniquity of the father, neither shall the father bear the iniquity of the son: the righteousness of the righteous shall be upon him, and the wickedness of the wicked shall be upon him.” If the son is capable of making his own decisions, he bears his own guilt.
Since parents are commanded to bring up their children “in the nurture and admonition of the Lord,” (Ephesians 6:4) it appears that parents may be held accountable for what they teach their children. If a parent knows what is right, but instead teaches the child to do wrong, then the parent must bear some blame. But that blame is for the teaching, not for the actions of the child. Once the child is able to know right from wrong he becomes accountable for his own choices. If those choices are based on wrong teaching then the teacher bears at least some guilt.
That a man may have to answer for his children while they are under his control is shown in the qualifications of elders and deacons. An elder must be “one that ruleth well his own house, having his children in subjection with all gravity; (for if a man know not how to rule his own house, how shall he take care of the church of God?)” (1 Timothy 3:4-5) He must also have “faithful children not accused of riot or unruly.” (Titus 1:6) Deacons also are to rule “their children and their own houses well.” (1 Timothy 3:12) So a parent must answer in some way for his children while they are in his household, and may suffer consequences if they are not obedient.
So there you have three different answers, depending on what you meant by your question.