Charcoal, 38 bytes

≔⎇№θx…θ⌕θxθθ≔⁰ηＦθ≡ιn≦⊕ηd≦⊖ηm≦⊗ηh≦⊘ηrＩη

Try it online! Link is to verbose version of code. Inspired by @RickHitchcock's answer. Explanation:

≔⎇№θx…θ⌕θxθθ

Truncate the input at the x if there is one. (I tried using a while loop but for some reason the variable got reset after the end of the loop, and an if requires an else so isn't very golfy.)

≔⁰η

Clear the variable.

Ｆθ≡ι

Loop over and switch on each character of the remainder of the input.

n≦⊕η

n increments the variable.

d≦⊖η

d decrements the variable.

m≦⊗η

m multiplies the variable by two (i.e. doubles).

h≦⊘η

h halves the variable.

rＩη

r prints the variable cast to string.

Charcoal, 37 35 bytes

≔⁰ηＦ⎇№θx…θ⌕θxθ≡ιn≦⊕ηd≦⊖ηm≦⊗ηh≦⊘ηrＩη

Try it online! Link is to verbose version of code. Inspired by @RickHitchcock's answer. Explanation:

≔⁰η

Clear the variable.

Ｆ⎇№θx…θ⌕θxθ≡ι

Truncate the input at the x if there is one, then loop over and switch on each character of (the remainder of) the input.

n≦⊕η

n increments the variable.

d≦⊖η

d decrements the variable.

m≦⊗η

m multiplies the variable by two (i.e. doubles).

h≦⊘η

h halves the variable.

rＩη

r prints the variable cast to string.

Charcoal, 37 bytes

Ｗ№θx≔…θ⌕θxθ≔⁰ηＦθ≡ιn≦⊕ηd≦⊖ηm≦⊗ηh≦⊘ηrＩη

Try it online! Link is to verbose version of code. Inspired by @RickHitchcock's answer. Explanation:

Ｗ№θx≔…θ⌕θxθ

Truncate the input at the x if there is one. (While is golfier than if as it doesn't need an else.)

≔⁰η

Clear the variable.

Ｆθ≡ι

Loop over and switch on each character of the remainder of the input.

n≦⊕η

n increments the variable.

d≦⊖η

d decrements the variable.

m≦⊗η

m multiplies the variable by two (i.e. doubles).

h≦⊘η

h halves the variable.

rＩη

r prints the variable cast to string.

Charcoal, 38 bytes

≔⎇№θx…θ⌕θxθθ≔⁰ηＦθ≡ιn≦⊕ηd≦⊖ηm≦⊗ηh≦⊘ηrＩη

Try it online! Link is to verbose version of code. Inspired by @RickHitchcock's answer. Explanation:

≔⎇№θx…θ⌕θxθθ

Truncate the input at the x if there is one. (I tried using a while loop but for some reason the variable got reset after the end of the loop, and an if requires an else so isn't very golfy.)

≔⁰η

Clear the variable.

Ｆθ≡ι

Loop over and switch on each character of the remainder of the input.

n≦⊕η

n increments the variable.

d≦⊖η

d decrements the variable.

m≦⊗η

m multiplies the variable by two (i.e. doubles).

h≦⊘η

h halves the variable.

rＩη

r prints the variable cast to string.