#### Answer

please see image
(graph of g(x) is red)
.

#### Work Step by Step

$f(x)=\sqrt{x}$
Using desmos.com, we graph f(x) (blue dashed graph)
By hand,
we select some values for x and make a table with
x ... f(x) as columns.
Each pair gives a point on the graph of f(x).
(In the screenshot, the table is to the left )
Plotting the points (x,f(x)) and joining them with a smooth curve, we have the graph of f(x).
Using Table 2.4, Summary of Transformations, we see that
$g(x)=2\sqrt{x+2}-2=2f(x+2)-2$
is obtained by
"Horizontal shifts $y=f(x+c)$
Shift the graph of $f$ to the left $c$ units."
"Vertical stretching or shrinking, $ y=cf(x),\ c > 1$
Multiply each y-coordinate of $y=f(x)$ by $c$,
vertically stretching the graph of $f$. "
and
"Vertical shifts, $ y=f(x)-c$
Lower the graph of $f$ by $c$ units.
$c$ is subtracted from $f(x)$."
So,
using our table (x, f(x))
We plot the points ( $x-2,\ 2f(x)-2$ ),
moving the originals to the left,
double their f(x) coordinate (stretch vertically),
and then shifting them down.
Join them with a smooth curve,
(red solid line on the screenshot),
and we have the graph of g(x).