Suppose you have a 150-kg wooden crate resting on a wood floor. (a) what maximum force (in n) can you exert horizontally on the crate without moving it?

Missing detail:
The coefficient of static friction is not specified in the problem. Searching online, I found that for wood-on-wood contact it is between 0.25-0.5. I assume here the maximum value, 0.5.

Solution:
When pushing the crate horizontally with a force F, only two forces act horizontally on the crate: F and , the frictional force, which points into the opposite direction of F and whose magnitude is given by

where  is the coefficient of static friction,  is the mass of the crate and  is the gravitational acceleration.

In order to start to move the crate, the force F applied must overcome the frictional force. This means that the minimum value of F necessary is equal to Ff: