Question 1033772
The line would have to have the form 3x+4y = k for some undetermined constant k > 0, as wanted.
The x-intercept of this line is k/3, while its y-intercept is k/4.

The area is thus {{{6 = (1/2)(k/4)(k/3) = k^2/24}}} 

==> {{{k^2 = 144}}} ==> k = 12.

Therefore the equation of the line is 3x+4y=12.