Answer :

Let's solve the given mathematical expressions step by step:

### Expression 1: [tex]\( a + b - c \)[/tex]

1. We are given the values:
- [tex]\( a = 2 \)[/tex]
- [tex]\( b = 3 \)[/tex]
- [tex]\( c = 4 \)[/tex]

2. Substitute these values into the expression [tex]\( a + b - c \)[/tex]:
[tex]\[ a + b - c = 2 + 3 - 4 \][/tex]

3. Perform the arithmetic operations:
[tex]\[ 2 + 3 = 5 \][/tex]
[tex]\[ 5 - 4 = 1 \][/tex]

So, the result of the expression [tex]\( a + b - c \)[/tex] is [tex]\( 1 \)[/tex].

### Expression 2: [tex]\( 4x^3 + 6x^2 - x - 8 \)[/tex]

1. We are given the value:
- [tex]\( x = 1 \)[/tex]

2. Substitute this value into the polynomial expression:
[tex]\[ 4x^3 + 6x^2 - x - 8 \][/tex]
[tex]\[ 4(1)^3 + 6(1)^2 - 1 - 8 \][/tex]

3. Compute each term individually:
[tex]\[ 4(1)^3 = 4 \cdot 1 = 4 \][/tex]
[tex]\[ 6(1)^2 = 6 \cdot 1 = 6 \][/tex]
[tex]\[ -x = -1 \][/tex]
[tex]\[ -8 = -8 \][/tex]

4. Combine these results:
[tex]\[ 4 + 6 - 1 - 8 \][/tex]
[tex]\[ 4 + 6 = 10 \][/tex]
[tex]\[ 10 - 1 = 9 \][/tex]
[tex]\[ 9 - 8 = 1 \][/tex]

So, the result of the polynomial [tex]\( 4x^3 + 6x^2 - x - 8 \)[/tex] when [tex]\( x = 1 \)[/tex] is [tex]\( 1 \)[/tex].

Therefore, the final answers for the given expressions are:
1. [tex]\( a + b - c \)[/tex] is [tex]\( 1 \)[/tex]
2. The polynomial [tex]\( 4x^3 + 6x^2 - x - 8 \)[/tex] evaluated at [tex]\( x = 1 \)[/tex] is [tex]\( 1 \)[/tex]