手を出す (to get involved / make a move)

A context-dependent idiom literally 'to put out one's hand,' with figurative senses: 'to get involved with / dabble in / mess with' (something risky or off-limits), 'to make a move on' (romantic/sexual), 'to strike / attack' (physical), or 'to meddle / interfere' (social). Context determines the sense.