Question 178826
Let's make a table of each coin toss and whether its a heads or tail (H or T). 
Then in the last column, sum the number of heads in all four tosses. 
4 coins with 2 sides gives 16 possible outcomes. 

H	H	H	H	4
H	H	H	T	3
H	H	T	H	3
H	H	T	T	2
H	T	H	H	3
H	T	H	T	2
H	T	T	H	2
H	T	T	T	1
T	H	H	H	3
T	H	H	T	2
T	H	T	H	2
T	H	T	T	1
T	T	H	H	2
T	T	H	T	1
T	T	T	H	1
T	T	T	T	0

Of the 16, only 6 have exactly 2 heads. 
That means you would win 6/16 times, and lose 10/16 times. 
No, the game is not fair to you. 
The other player has the advantage.
If it was fair, both would have 8/16 or 1/2 of the possible outcomes.