From https://metaculus.com/questions/16743/ukraine-regains-bakhmut-before-june-2023/

Some 10½ months ago, on February 24th, 2022, Russia invaded Ukraine. Their concept of operations apparently involved rapidly taking the capital, deposing the government, and largely completing the country's conquest before Western countries could co-ordinate on a reaction. By April 2022, after fierce Ukrainian resistance and serious deficiencies in Russian military preparedness defeated this plan, Russia shifted focus to the Donets Basion (Donbas) region in the country's east, where conditions were more favorable. This offensive also bogged down quickly, and Russia's offensive ambitions continually narrowed into the summer until they were focused ultimately around the town of Bakhmut, where operations were being conducted largely by the "Wagner Group" private army under Yevgeny Prigozhin instead of by the regular Russian army.

By fall, Bakhmut was described as an obsession for Russia and a "meat grinder" into which its best forces were being wastefully thrown. Nonetheless, the Bakhmut offensive continued, with some analysts speculating that it was essentially a propaganda operation designed to provide Russian President Putin with a "victory" to offset mounting defeats, or even motivated by Prigozhin's personal financial interests.

On December 20th, Ukrainian President Volodymyr Zelenskyy visited Bakhmut to show support for the defenders. On January 6th, Russia launched a powerful assault on the adjacent town of Soledar, where Ukrainian officials acknowledged the situation was "difficult.".

After months of fighting Russia made incremental gains in Bakhmut, with the city administrative building allegedly falling to Russian troops in April.

On May 5, the head of the Wagner Group, the Russian paramilitary organization leading the offensive, said that Wagner would withdraw from the battle because of lack of Russian support.