How many non-negative integer values of ‘x’ are possible for the equation x2 – 4|x| + |a – 4| = 0, where ‘a’ is an integer?

The given equation is x^2 - 4|x| + |a - 4| = 0.

Let's solve this step by step:

Step 1: We know that x^2 is always non-negative and 4|x| is also always non-negative. Therefore, for the equation to hold true, |a - 4| must also be non-negative.

Step 2: The term |a - 4| can be 0 only when a = 4. In this case, the equation becomes x^2 - 4|x| = 0. This equation has two solutions: x = 0 and x = 4.

Step 3: If |a - 4| > 0, then the equation becomes x^2 - 4|x| + some positive number = 0. This equation has no solution because x^2 - 4|x| is always non-negative and cannot equal a negative number.

So, there are 2 non-negative integer solutions for x: 0 and 4.