What does Ruth 4:8 mean?

The matter is settled. The nearer kinsman-redeemer will not buy Naomi's land nor marry Ruth, thus avoiding the risk that Ruth could have many sons and threaten his own sons' inheritance (Ruth 4:1–6). If Boaz is willing to take those responsibilities, that is fine.

There is no shame in his decision. He's right that if Ruth had children, it would cost him. By law, as the next of kin, he is responsible for buying Naomi's land (Leviticus 25:25) but Boaz's addition of a levirate marriage with Ruth is more manipulative than lawful. In the Mosaic law, he's also well within his rights to refuse to marry a Moabite woman (Deuteronomy 23:3–6). It's a fine line, however, because of the honor-shame culture of the ancient middle east. To take the land without providing the opportunity for its redemption would be legal, but not a "good look." Even though Ruth is a Moabitess, she swore to leave her people and gods and take Naomi's (Ruth 1:16–17; 2:11–12). The entire town of Bethlehem respects her (Ruth 3:11).

Fortunately, Boaz offers the man a way out: if the next of kin doesn't want the land or Ruth, Boaz is more than willing to take responsibility (Ruth 3:13). The man finishes the transaction by legally declaring his intent before the ten elders (Ruth 4:2) and performing the obscure tradition of presenting Boaz with his sandal (Ruth 4:7). He is mentioned no more.

Most importantly, Boaz can now complete Ruth's plan of providing Naomi with everything she needs and proving that Yahweh did not abandon her.