25011

You would solve it by creating equations and then substitution.

1. First you would find the two lines that have the same shapes in them.
I am going for the top row and the second column:

s + t = 14
s + t + 2s = 30
= 14 + 2s = 30 ( as s + t = 14, substitute that answer into the 2nd equation.)
2s = 16
Square =8

Then you would substitute s into equation 1: 8 + t = 14
t = 6
Triangle = 6

2. The next two I am going for are the 2nd row and the third column.

2nd row:
16 + 2h = 30
2h = 14
h = 7
Hexagon = 7

3rd column:
8 + 7 + 2c = 23
15 + 2c = 23
2c = 8
c = 4
Circles = 4

So the full set of symbols and their corresponding values are:
Square=8
Triangle = 6
Hexagon = 7
Circles = 4

So the missing total is 6 + 7 + 4 + 4 = 21