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6 person do a job in 6 days 1 person do the same job in 6*6 = 36 days 2 person in 36/2 = 18 days

Another way -

6 person day job in 6 days so in day they do 1/6 of the total work 1 person in one day will do 1/6*6 = 1/36 of total work so 2 person in one day will do 2/36 = 1/18 of total work Hence, 2 person will take 18 days to finish the same job

Red part is not correct: 6 people need 6 days to do the job; 6 people in one day do 1/6 of the job; 1 person in one day does 1/6*6=1/36 of the job.

2 persons in 1 day do 2*1/36=1/18 of the job. To do the whole job the'll need 18 days.

But the above can be done in easier way: Time, rate and job in work problems are in the same relationship as time, speed (rate) and distance.

Time*Rate=Distance Time*Rate=Job

We are told that combined rate decreased 3 times, therefore to do the same job, it would take 3 times more days (time). So, now it would take 6*3=18 days.