First find the total area of the forest: 4 miles * 6 miles = <<4*6=24>>24 square miles
Then find the total number of trees in that area: 600 trees/square mile * 24 square miles = <<600*24=14400>>14400 trees
Then find the number of trees all the loggers can cut down in one day: 8 loggers * 6 trees/logger = <<8*6=48>>48 trees
Then divide the total number of trees by the number cut down per day to find the number of days it takes to clear the forest: 14400 trees / 48 trees/day = <<14400/48=300>>300 days
Then divide the time in days by the number of days per month to find the time in months: 300 days / 30 days/month = <<300/30=10>>10 months
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