First, add #color(red)(6)# to each segment of the system of inequalities to isolate the #t# term while keeping the system balanced:

#-4 + color(red)(6) < 2t - 6 + color(red)(6) < 8 + color(red)(6)#

#2 < 2t - 0 < 14#

#2 < 2t < 14#

Now, divide each segment by #color(red)(2)# to solve for #t# while keeping the system balanced:

#2/color(red)(2) < (2t)/color(red)(2) < 14/color(red)(2)#

#1 < (color(red)(cancel(color(black)(2)))t)/cancel(color(red)(2)) < 7#

#1 < t < 7#

Or

#t > 1# and #t < 7#

Or, in interval notation:

#(1, 7)#

To graph this we will draw vertical lines at #1# and #7# on the horizontal axis.

The lines will be dashed lines because both inequality operators do not contain an **"or equal to"** clause.

We will shade between the lines to show the interval: