y=log4(x+3).
Make a table of x and y values, and choose x so that the log4 is easy to work out. For example:
x y
-3 -∞ x=-3 is an asymptote
-2 0
-1 0.5
1 1
13 2
61 3
Plot these points and join them up first by using straight lines, then by imagining and sketching the curve that would pass through them all.
The red curve is y=log4(x+3) and the blue line is the asymptote.