A winch-winding assembly for use with a flatbed winch, for example. The winch-winding assembly can be used for winding tie-down straps. The winch-winding assembly can include a gear system, a drive shaft connected to the gear system in order to cause rotation of the gear system and an engagement arm being configured to engage with and rotate part of the flatbed winch. A drill-support mechanism can be further provided to guide or support a body of a hand-held drill during engagement and rotation of the drive shaft. The engagement arm can comprise a stem and a finger mounted to the stem and being displaceable between a retracted position disengaging the flatbed winch, and an extended position engaging the flatbed winch, to rotate the winch drum in response to rotation of the stem.