First find the slope of the given line. 6x+4y=3. Isolate y. 4y=-6x+3, y=-3/2x+3/4.
The slope is -3/2. A perpendicular slope would equal the negative reciprocal of -3/2, which is 2/3.
The answer would be any line with a slope of 2/3 (ie y=2/3x-1).
To check, graph the given and derived equation.