Turn Halfway

In Scottish Country Dancing Turn halfway means that the dancers Exchange positions and Finish Facing each other; it is a synonym for one of the meanings of Cross.
Unless qualified, it means By the right.

For example, here are some Scottish Country Dances in which the term, Turn halfway, is used in either the Minicrib or the Maxicrib Dance instructions or both -
Above The Clouds
Dancers' Wedding
Deuks Dang Ower My Daddie.
Dophei Strathspey
Hana Strathspey
Jig For Ann
Lost In Edinburgh.
Miss Allie Anderson
Mrs Stuart Linnell.
Old Spedling Castle's Ghost's Dance.

Figures

Turning

Birl
Open Turn
Pump Handle Turn
Quick Turn
Slow Turn
Tulloch Turn
Turn
Turn Both Hands
Turn By The Left
Turn By The Left Halfway
Turn By The Right
Turn By The Right Halfway
Turn Corner, Partner, Corner, Partner
Turn Halfway
Turn On The Spot Halfway