if the carpenter can do the whole job in 4 hours, that means in 1 hour, it has only done 1/4 of the whole thing.
if his assistant can do the job in 6 hours, that means, in 1 hour, he has done only 1/6 of the whole job.
let's say if both of them work together, they can do the job in "t" hours, so in 1 hour alone, the carpenter has done 1/4 of it, and the assistant has done 1/6 of it, for a total of 1/t of the job.
[tex]\bf \stackrel{\textit{carpenter's rate}}{\cfrac{1}{4}}+\stackrel{\textit{assistant's rate}}{\cfrac{1}{6}}~~=~~\stackrel{\textit{total done}}{\cfrac{1}{t}}
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\cfrac{3+2}{12}=\cfrac{1}{t}\implies \cfrac{5}{12}=\cfrac{1}{t}\implies 5t=12\implies t=\cfrac{12}{5}\implies \stackrel{\textit{2 hours and 24 minutes}}{t=2\frac{2}{5}}[/tex]
