(-3, 2)⋃[1, 4)

Put (-3,2) on a number line:

---------⚪==================⚪----------------
-5  -4  -3  -2  -1   0   1   2   3   4   5   6

Put [1,4) on a number line the same size:

-------------------------⚫===========⚪--------
-5  -4  -3  -2  -1   0   1   2   3   4   5   6

Write one number line under the other:

---------⚪==================⚪----------------
-5  -4  -3  -2  -1   0   1   2   3   4   5   6
-------------------------⚫===========⚪--------
-5  -4  -3  -2  -1   0   1   2   3   4   5   6

Now since it's ⋃ and not ⋂,

the graph of the answer is gotten by shading all that parts 
that is shaded on ONE GRAPH OR THE OTHER,

So the graph is

---------⚪===========================⚪-------
-5  -4  -3  -2  -1   0   1   2   3   4   5   6

which in interval notation is (-3,4)

*****************************************************
*****************************************************

By the way, if the problem had been 

(-3, 2)⋂[1, 4) instead

we would have gotten to this step as above:

---------⚪==================⚪----------------
-5  -4  -3  -2  -1   0   1   2   3   4   5   6
-------------------------⚫===========⚪-------
-5  -4  -3  -2  -1   0   1   2   3   4   5   6

but then the graph of the answer would have been gotten
by shading ONLY that part that is shaded on BOTH graphs:

-------------------------⚫==⚪----------------
-5  -4  -3  -2  -1   0   1   2   3   4   5   6

and the answer in interval notation would have been [1,2).

You will no doubt have problems like that too.

Edwin