Please help. I don't understand.

3/8 ths x    on racket    -    1/8x on watch   = 14

3/8 x - 1/8 x = 14

2/8 x = 14

x = 14 * 8/2 = 14 * 4 = 56 dollars  initially   

(3/8 + 1/4)  56 = 35 dollars total

How much money did Henry spend on the two items altogether?

Hello Guest!

Henry owns x.

$\color{blue}\frac{x}{8}+$14=\frac{3x}{8}\\ \frac{3x-x}{8}=$14\\ 2x=$112$

$x=$56$

$(\frac{1}{8}+\frac{3}{8})\cdot $56=\color{blue}$28$

$28 did Henry spend on the two items altogether.

  !

Straightforward. First, assign variables to the unknown values:

Let H = Henry’s money
Let B = Badminton Racket
Let W = Watch

We are given:
B = 3/8 H
W = 1/8 H
B = W + $14

So:
Substitute B and W:
3/8 H = 1/8 H + $14 [Cost of Badminton racket = $14 more than cost of watch]

Solving:
3/8 H - 1/8 H = $14
(3/8–1/8) H = $14
2/8 H = $14
1/4 H= $14
H = 4 * $14 = $56 [Henry’s total money]
B = 3/8 * $56 = $21 [Cost of badminton racket]
W = 1/8 *$56 = $7 [Cost of watch]

Check:
B = W + $14
$21 =? $7 + $14
Yes! 

Henry spent B+W on his items altogether, which is $21+$7 = $28.

Another way of expressing it is:
2/8 H = $14
1/8 H = $7

B+W = 3/8 H + 1/8 H = (3+1)/8 H = 4/8 H = 1/2 H.
H = $56
B+W = 1/2 H = $28