To solve the first equation, we need to distribute the 0.2 to both terms inside the parentheses on the left side:

0.2(9) + 0.2(2+x) = 2.4
1.8 + 0.2(2+x) = 2.4

Now distribute the 0.2 again:
1.8 + 0.4 + 0.2x = 2.4

Combine like terms:
2.2 + 0.2x = 2.4

Subtract 2.2 from both sides:
0.2x = 0.2

Divide by 0.2 to solve for x:
x = 1

Now, to solve the second equation:
5.1(14-x) = 10.2

Distribute the 5.1:
71.4 - 5.1x = 10.2

Subtract 71.4 from both sides:
-5.1x = -61.2

Divide by -5.1 to solve for x:
x = 12

So the solutions are x = 1 and x = 12.