I do not know what you mean by the "conflict" for this story.
But here is the plot:
A grand father got so old that his legs didn't work any more, he was blind, deaf, and he didn't have any teeth. His daughter-in-law got tired of the mess he would make at the table, so she made him eat behind the stove out of a cup. One day he fumbled with the cup and broke it, making a mess. The daughter-in-law began grumbling about that and said from now on she would feed him from a wash pan.
A day or so later the daughter-in-law and son were watching the grand son play with blocks on the floor in their home. The boy was obviously building something with a concentrated passion. His father asked him what he was building. The small boy replied, "Why, Mother, Father, I am building a wash pan, for when you get old I will be able to feed you from."
The daughter-in-law and son began to cry and held their heads in shame. From then on they set a place at the table for the old man, and the daughter-in-law no longer grumbled as she had about the messes the old grand father made. (Leo Tolstoy)
This story has been told in different versions. This is just a general Idea of the plot. : )