I'd be happy to help you out with this. :)
Alright so when you are dealing with equations such as the one you have here:
x + 3 = -6
You want to solve for the variable, in this case x. In order to do that you need to get the variable by itself. So what I would do is subtract the 3 from both sides.
x + 3 = -6
-3 -3
-------------
x = -9
For the second problem:
12 + x = -7 You do the same thing, get the variable, x, by itself. To do this subtract 12 from both sides.
12 + x = -7
-12 -12
---------------
x = -19
For the third problem: t + 1/2 = 3/4 you are dealing with fractions, but the idea is the same. Get the variable by itself by subtracting 1/2 from both sides:
t + 1/2 = 3/4
-1/2 -1/2
----------------
t = 3/4 - 1/2
Now you want to combine like terms but in order to add or subtract fractions you must first get a common denominator.
In this case the common denominator would be 4 so the only fraction that you have to change is the 1/2.
Multiply 1/2 by 2/2
1/2 * 2/2 = 2/4
The new equation is:
t = 3/4 - 2/4
Now you can subtract 2/4 from from 3/4:
3/4 - 2/4 = 1/4
t = 1/4
There are the solutions and explanations to all your questions, if you need any more help, please don't hesitate to ask me. Have a great day and happy problem solving :D