To simplify the given expressions, we can factor or complete the square as needed. Here’s the work for each expression:

a) \( A = x^2 + 6x + 12 \)
- Completing the square:
\[
A = (x + 3)^2 + 3
\]

b) \( B = 3x^2 - 12x + 15 \)
- Factoring out the common factor:
\[
B = 3(x^2 - 4x + 5) = 3((x - 2)^2 + 1) = 3(x - 2)^2 + 3
\]

c) \( C = x^4 - 6x^2 + 10 \)
- Let \( y = x^2 \):
\[
C = y^2 - 6y + 10
\]
- Completing the square:
\[
C = (y - 3)^2 + 1 = (x^2 - 3)^2 + 1
\]

d) \( D = x^4 + 4x^2 + 2 \)
- Let \( y = x^2 \):
\[
D = y^2 + 4y + 2
\]
- Completing the square:
\[
D = (y + 2)^2 - 2 = (x^2 + 2)^2 - 2
\]

e) \( E = (x + 2)^2 + (x - 2)^2 \)
- Expanding:
\[
E = (x^2 + 4x + 4) + (x^2 - 4x + 4) = 2x^2 + 8 = 2(x^2 + 4)
\]

f) \( F = (3x - 2)^2 + (4x + 3)^2 \)
- Expanding:
\[
F = (9x^2 - 12x + 4) + (16x^2 + 24x + 9) = 25x^2 + 12x + 13
\]

g) \( G = x^2 + y^2 + 2x - 4y + 9 \)
- Completing the square for both variables:
\[
G = (x + 1)^2 + (y - 2)^2 + 6
\]

h) \( H = 2x^2 + y^2 + 2xy + 2x - 4y + 19 \)
- Reorganizing and completing the square:
\[
H = 2(x^2 + x) + (y^2 + 2xy - 4y) + 19
\]
- Completing the squares:
\[
H = 2\left(x + \frac{1}{2}\right)^2 - \frac{1}{2} + (y - x - 2)^2 + 19
\]

If you need further adjustments or specific factorizations, let me know!