I think you mean 4x2+24x+4y2-32y+51=0.
The best way is to determine where the centre is and what the radius is. To do this, we need to complete the squares for x and y:
4(x2+6x+9-9)+4(y2-8y+16-16)+51=0.
Here we halve the x term's coefficient then square it, so 6/2=3 and 32=9. x2+6x+9=(x+3)2, but we added 9 so, to balance the equation we have to subtract 9, which will be included in the final constant. Do the same with y: 8/2=4 and 42=16. Now we can write the equation as:
4(x+3)2-36+4(y-4)2-64+51=0,
4(x+3)2+4(y-4)2-100+51=0,
4(x+3)2+4(y-4)2-49=0,
(x+3)2+(y-4)2=49/4, which tells us that the centre of the circle is at (-3,4) and the radius=√(49/4)=7/2 (3.5).
You can now use a pair of compasses to draw the circle on graph paper.