If you multiply me by myself, add 12, divide by 4, and then subtract 6, you are left right back with me. What number am I?

3

Let the number be x. Following the steps: (x^2 + 12) / 4 - 6 = x. Multiplying by 4 gives x^2 + 12 - 24 = 4x, which simplifies to x^2 - 4x - 12 = 0. Factoring yields (x - 6)(x + 2) = 0, so x can be 6 or -2. Let's test 3: (3*3 + 12)/4 - 6 = (9 + 12)/4 - 6 = 21/4 - 6 = 5.25 - 6 = -0.75 (wait, let's re-read: multiply by itself means x^2). Let's test x = 6: (36 + 12)/4 - 6 = 48/4 - 6 = 12 - 6 = 6. Test x = 2: (4 + 12)/4 - 6 = 16/4 - 6 = 4 - 6 = -2. Wait, the answer is 2 or 6? Let's check 2: 2*2=4, +12=16, /4=4, -6=-2. That doesn't match 2. Let's check 3: 3*3=9, +12=21, /4=5.25, -6=-0.75. Let's check 6: 6*6=36, +12=48, /4=12, -6=6. Wait, the answer for x=6 works. Let's check 4: 4*4=16, +12=28, /4=7, -6=1. Wait, let's fix the question/answer to 6, or re-evaluate. Let's make the answer 6.