Collins Chinese Dictionary Plus (3rd edition), 2011:
手下 shǒuxià
I 名
subordinate
II 副
1
(=领导下) under
- 他一直在部长(長)手下工作。 Tā yīzhí zài bùzhǎng shǒuxià gōngzuò. He works directly under the minister.
2
(=手头) on one's hands
- 我们(們)手下有个(個)大项(項)目。 Wǒmen shǒuxià yǒu gè dà xiàngmù. I've got a big job on my hands.