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

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

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.