let

p = the united ages of man and wife

c = the united ages of their children

n = the number of children

the united ages of a man and wife are at present six times those of their children

p = 6c

two years ago,their united ages were ten times the united ages of their children

p - 2*2 = 10(c - 2n)

6 years hence, they will be three times the united ages of their children

p + 6*12 = 3(c + 6n)

by solving the system of equations

p = 6c

p - 2*2 = 10(c - 2n)

p + 6*12 = 3(c + 6n)

we find

n = 3 children

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they have 3 children.