Just do it the same way as you normally would.

Usually, binomial expansion is shown like (a + b) ^ 12

Here, you just substitute the variables

a = x^2 (yes, I know substituting variables with variables doesn't make sense)

b = -1

So normally,

(a + b)^12 = a^12 + 12a^11b + 66a^10b^2 + 220a^9b^3 + 495a^8b^4 + 792a^7b^5 + 924a^6b^6 + 792a^5b^7 + 495a^4b^8 + 220a^3b^9 + 66a^2b^10 + 12ab^11 + b^12

Just substitute (too lazy, I used Find & Replace, there may be mistakes)

(x^2-1)^12 = (x^2)^12 + 12(x^2)^11(-1) + 66(x^2)^10(-1)^2 + 220(x^2)^9(-1)^3 + 495(x^2)^8(-1)^4 + 792(x^2)^7(-1)^5 + 924(x^2)^6(-1)^6 + 792(x^2)^5(-1)^7 + 495(x^2)^4(-1)^8 + 220(x^2)^3(-1)^9 + 66(x^2)^2(-1)^10 + 12(x^2)(-1)^11 + (-1)^12

Oh god, this is gonna be long...but there's a pattern, so it's not so bad...

x^24 -12x^22 + 66x^20 - 220x^18 + 495x^16 - 792x^14 + 924x^12 - 792x^10 + 495x^8 - 220x^6 + 66x^4 - 12x^2 + 1

By pattern, I meant that + and - alternate because of the -1. The exponent on x also goes down by 2 each time, since it's x^2.

Hope I helped!