Question 56354
{{{ -8x+12y=48}}} and {{{ 2x-3y=6 }}}
get both equations in y=mx+b (point-slope form)
{{{ 12y = 8x +48 }}} and {{{ -3y =-2x +6 }}}
divide the first by 12 and divide the second by -3
{{{ y = 8x/12 +48/12 }}} and {{{ y =-2x/-3 +6/-3 }}}
Reduce the fractions
{{{ y = 2x/3 + 4 }}} and {{{ y =2x/3 -2 }}}
Notice how the m value IS exactly the same.  so assuming your wrote the problem correctly .. they ARE parallel.
{{{ graph( 300, 300, -5, 5, -5, 5, (2x/3)+4, (2x/3)-2 ) }}}