8less than the product of -3 and anumber is greater than -26.

8 less than  means -8
product of means multiplication of some things
product of -3 and a number means -3 times a number
is greater than  means >
-26 so
-8+-3 times a number>-26
solve for 'a number'
add 8 to both sides
-3 times a number>-18
divide both sides by -3
remember tha twhen you divide or multiply by a negative, the inequality sign flips
a number<6
so the number is less than 6

The inequality expression would be: -3x - 8 > -26
    
-3x - 8 > -26
      + 8    + 8
-3x      > -18
÷ -3         ÷-3
    x     >  6   ⇒ becomes x < 6

Notice the change in the inequality sign? This flip is done when the division and multiplication is made by a negative number. In this case, -3 is the divisor.
It is generally done during the first part of the inequality. However, to avoid confusion, flipping the inequality sign is done at the end of the solution.
Assuming: x = 5

-3(5) - 8 > -26
-15 - 8 > -26
-23 > -26