https://desktop.arcgis.com/en/arcmap/latest/tools/analysis-toolbox/tabulate-intersection.htm
Zone features - your polygons
Zone Field - something you can use to identify later
Class feature - Lines
class fields - something to identify by later
Then take that output table and use the Pivot Table tool (exactly how to do this is shown in the tool help link above)
Note needs Advanced license. If you don't have one then https://esriaustraliatechblog.wordpress.com/2015/06/22/spatial-joins-hidden-trick-or-how-to-transfer...
but you'll need to do wrangling with the concatenated field. Also top tip is to make sure the field length in the output field properties (shown if you read the guide fully) is long enough to store all the possibilities (from experience..)
