How many synapses does a nervous signal have to cross when moving from an interneuron in the spinal cord to activate an effector organ for the somatic motor division?

Two synapses.

Explanation:

Synapse or Synaptic cleft is the space two neurons or between a neuron or target organ where the signal is carried by neurotransmitter. Nerve signal first travel through interneuron to motorneuron passing through the first synapse, then the signal will travel to effector organ from motor neuron by passing through second synapse.