Mfcttrf

The function I am trying to plot is y = frac6x^2-3x+42x^2-8

documentclassarticle
usepackage[utf8]inputenc
usepackagetitling
usepackageamssymb
usepackagepgfplots

begintikzpicture
 beginaxis
 [
 title = Graph of $frac6x^2-3x+42x^2-8$,
 axis lines = center,
 xlabel = $x$,
 ylabel = $y$,
 ]
 addplot[color=red]y = frac6x^2-3x+42x^2-8;
 endaxis
endtikzpicture

I am new to LaTex and I've been trying to follow other answers on here, but I'm still a bit confused. Apologies for posting a duplicate.

Edit: Sorry if I wasn't clear, here is how it's supposed to look.

You can try the following, if you want a smoother plot, just increase the number of points.

documentclassarticle
usepackagepgfplots
pgfplotssetcompat=1.16

begindocument

begintikzpicture
 beginaxis
 [
 title = Graph of $frac6x^2-3x+42x^2-8$,
 axis lines = center,
 xlabel = $x$,
 ylabel = $y$,
 ]
 addplot[color=red] (6*x^2-3*x+4) / (2*x^2-8) ;
 endaxis
endtikzpicture

enddocument

Edit:

As I said, you can increase no. points by samples=<..> and also you can limit ymin and ymax because you have two infinite discontinuities at ±2:

begintikzpicture
 beginaxis
 [
 title = Graph of $frac6x^2-3x+42x^2-8$,
 axis lines = center,
 xlabel = $x$,
 ylabel = $y$,
 samples=500,
 ymin=-150, ymax=150,
 ]
 addplot[color=red] (6*x^2-3*x+4) / (2*x^2-8) ;
 endaxis
endtikzpicture

with plain TikZ:

documentclass[tikz,border=5mm]standalone
begindocument
begintikzpicture[yscale=1/30,xscale=1.2,
declare function=
f(x)=(6*x*x-3*x+4)/(2*x*x-8);
]
defxmin-4 defxmax4
defymin-100 defymax100

draw[->] (xmin,0)--(xmax,0) node[below]$x$;
draw[->] (0,ymin)--(0,ymax) node[right]$y$;
draw (2,ymax)--(2,ymin) (-2,ymax)--(-2,ymin);
draw[magenta,smooth,samples=100] 
plot[domain=-1.95:1.97] (x,f(x))
plot[domain=2.03:3.8] (x,f(x))
plot[domain=-3.8:-2.05] (x,f(x));
draw 
(0,50)--+(0:1mm)--+(180:1mm) node[left]$50$
(0,-50)--+(0:1mm)--+(180:1mm) node[left]$-50$;
path
(0,0) node[below left]O 
(2,0) node[below right]$2$
(-2,0) node[below left]$-2$
(current bounding box.north) node[above]
The graph of $y=frac6x^2-3x+42x^2-8$;
endtikzpicture
enddocument

Hasty attempt with MetaPost and LuaLaTeX, using an old template of my own.

documentclass[12pt,border=5mm]standalone
usepackageluatex85, luamplib
 mplibsetformatmetafun
 mplibtextextlabelenable
 mplibnumbersystemdouble
begindocument
beginmplibcode

vardef function(expr xmin, xmax, xstep)(text f_x) =
 save x; x := xmin;
 (x, f_x)
 forever: hide(x := x + xstep) exitif x > xmax;
 .. (x, f_x)
 endfor
 if x - xstep < xmax: hide(x := xmax) .. (x, f_x) fi
enddef;

u = v = .5cm;
xmax = -xmin = 15; ymax = -ymin = 20; xstep := .01;

vardef f(expr x) = (6(x**2)-3x+4)/(2(x**2)-8) enddef;

beginfig(1);

 drawoptions(withcolor green);
 draw (-2u, ymin*v) -- (-2u, ymax*v);
 draw (2u, ymin*v) -- (2u, ymax*v);
 draw (xmin*u, 3v) -- (xmax*u, 3v);

 drawoptions(withcolor red);
 draw function(xmin, -2.1, .xstep)(f(x)) xyscaled (u,v);
 draw function(-1.9, 1.95, xstep)(f(x)) xyscaled (u,v); 
 draw function(2.1, xmax, xstep)(f(x)) xyscaled (u,v);

 clip currentpicture to ((xmin, ymin) -- (xmax, ymin) -- (xmax, ymax) -- (xmin, ymax) -- cycle) xyscaled (u,v);

 drawoptions(withcolor black);
 drawarrow (xmin*u, 0) -- (xmax*u, 0);
 drawarrow (0, ymin*v) -- (0, ymax*v);

 for i = 1 upto floor(xmax.-1):
 draw (i*u, -2bp) -- (i*u, 2bp);
 draw (-i*u, -2bp) -- (-i*u, 2bp);
 endfor;

 for j = 1 upto floor(ymax-.1):
 draw (2bp, j*v) -- (-2bp, j*v);
 draw (2bp, -j*v) -- (-2bp, -j*v);
 endfor;

 label.bot("$x$", (xmax*u,0)); label.lft("$y$", (0, ymax*v));
 labeloffset := 5bp;
 label.bot("$-2$", (-2u,0)); label.bot("$2$", (2u, 0));
 label.lft("$3$", (0,3v));
endfig;

endmplibcode
enddocument