We are given:
\(\displaystyle\frac{{{10}-{3}\cdot{2}}}{{{1}+{1}}}\)

Use the order of operations: PEMDAS Parenthesces, Erponents, Multiplication, Division, Addition, Subtraction

Multiply on the numerator: =\(\displaystyle\frac{{{10}-{6}}}{{{1}+{1}}}\)

Subtract on the numerator: =\(\displaystyle\frac{{4}}{{{1}+{1}}}\)

Add on the denomunator: =\(\displaystyle\frac{{4}}{{2}}\)

Divide: =2

Use the order of operations: PEMDAS Parenthesces, Erponents, Multiplication, Division, Addition, Subtraction

Multiply on the numerator: =\(\displaystyle\frac{{{10}-{6}}}{{{1}+{1}}}\)

Subtract on the numerator: =\(\displaystyle\frac{{4}}{{{1}+{1}}}\)

Add on the denomunator: =\(\displaystyle\frac{{4}}{{2}}\)

Divide: =2