To simultaneously use two brushes to paint and write
To simultaneously approach a task from two directions
Neutral
治疗和锻炼双管齐下，他很快就会恢复健康 | Zhìliáo hé duànliàn shuāngguǎnqíxià, tā hěn kuài jiù huì huīfù jiànkāng
With medical treatment and exercise working in parallel, he will recover quickly
[Source]
总体而言，需要双管齐下，将政治和维和举措结合起来 | Zǒngtǐ ér yán, xūyào shuāngguǎnqíxià, jiāng zhèngzhì hé wéihé jǔcuò jiéhé qǐlái
Overall, a dual track was needed, combining both political and peacekeeping initiatives.
[Source]
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Multiple sources have different given names for the government official in the story. The name here was taken directly from the work from which this chengyu originated
《图画见闻志》(Tú Huà Jiàn Zhì), a work by Sòng Dynasty (宋, 960 - 1279) author 郭若虚 (Guō Ruò Xū)
In the Táng Dynasty (唐, 618 - 907), there was a government official named 张璪 (Zhāng Zǎo) who was an extremely skilled painter of nature scenes. In fact, he was so skilled at painting that he could simultaneously paint with a brush in each hand. This talent and the beautiful artwork produced astounded others, and they eventually began calling the painting style "双管齐下."