Question

How many solutions does the equation y + 12 = y + 10 + 2 have?

Answer 1

There are infinite solutions.
Think about it. The equation says essentially:
12 + any number = 12 + any number.
y + 12 = y + 10 + 2
y + 12 = y + 12
y - y = 12 - 12
0 = 12 - 12
0 = 0

Answer 2

y + 12 = y + 10 + 2

y + 12 = y + 12

y - y = 12 - 12

0 = 0

When solving an equation and you see the format 0 = 0, know that there are infinitely many solutions.

When you plug in any number at all for y, it would satisfy the original equation.

So the solutions are infinitely many.