What is ##14 + 18 -:2 * 18 -7##, using order of operations?

##14+18-:2xx18-7=color(blue)169##

is an anagram that helps us to remember the order of operations.

##14+18-:2xx18-7##

There are no parentheses or exponents, so we start with multiplication and division from left to right.

##14+color(red)(18-:2)xx18-7##

Carry out the division highlighted in red.

##14+color(red)(9)xx18-7##

Carry out the multiplication highlighted in blue.

##14+color(blue)(9xx18)-7##

Simplify.

##14+color(blue)(162)-7##

Simplify.

##169##