Selling Price = Buying Price + Profit

We know the selling price ($44 initially). Lets assume Buying price is $x.
i.e. 44 = x+10%x ==> 44 = x(1.1) ==> x = $40
So, the cost of the computer game is $40.

Now, the question states that the selling price increased to $46, but the cost remained the same. We need to find the percentage of the cost price (lets assume y is the %),

46 = 40 + 40*y% ==> 6 = 40*y% ==> y% = 6/40 ==> y% = 15%
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A simpler approach is to find the buying price (we got that as $40), then if 10% of $40 is $4 (making the selling price $44), and 20% of $40 is $8 (making the selling price $48), then 15% of 40 is $6 (making the selling price $46).

Hope that helps.