en_tn_lite_do_not_use/rut/04/10.md

in order that I might raise up the name of the dead man on his inheritance

The first son that Ruth bore would be legally considered Mahlon's son and would inherit the land that Boaz bought from Naomi. Alternate translation: "so that I might give her a son who will inherit the dead man's property"

so that his name will not be cut off from among his brothers and from the gate of his place

Being forgotten is spoken of as if one's name were being cut off from a list of people who had lived earlier. Alternate translation: "so that he will not be forgotten by his brothers' descendants and the people of this town" (See: rc://en/ta/man/jit/figs-metaphor)

the gate of his place

The gate of the town is where important legal decisions were made, such as decisions about who owns a piece of land.