Question 104442
In this problem, we are finding two unknowns. So we shall

Let x=the greater number
    y=the smaller number

The difference of the numbers is 12.

So, x-y=12

From which, x=y+12

Two fifths of the greater number is six more than one third of the lesser number

So, {{{(2/5)*x=(1/3)*y+6}}}

To eliminate the fractions, let us multiply both sides by 15.

{{{15*((2/5)*x)=15*((1/3)*y+6)}}}
~~~~~~{{{6x=5y+30}}}


But, x=y+12, so,

{{{6*(y+12)=5y+30}}}
~~~{{{6y+72=5y+30}}}

Subtracting 30 both sides,

{{{6y+42=5y}}}
~{{{y+42=0}}}
~~~~{{{y=-42}}}

Again, x=y+12, so,

x=y+12
x=-42+12
x=-30


Therefore, the two numbers are -30 and -42!