The distance from Mount Clinton Road parking area (which I believe is slightly farther that from the Highland center) to Mount Washington is about 8.4 miles.
Elevation gain is about 4700 feet. It's something like 2.9 miles to Mizpah hut then, including the summits about 5.5 miles.
By the way, I read the earlier posts in this thread and wanted to share with you that my 6 yr. old son and 8 yr. old daughter hiked with me up Tuck's trail, up the headwall crossed over through the Alpine Garden and down Lion's Head Trail which is somewhere around 7 miles and they did great. Sore legs and needing some encouragement...yes, but they loved every minute of it and can't wait to do it again!