How negative sign appeared out of nowhere?

[Benjamin_harsh]

Homework Statement

Determine the required magnitude of force F in the resultant couple
moment on the frame is 200 lb.ft clockwise.

Relevant Equations

$\Sigma F_x = \textbf{-}2*\frac{4F}{5}$

I have to find resultant for this couples:

My sir resolved given forces into components like this:

He considered Fx couples for sides 3,4,5 triangles:

He wrote resultant force for this above diagram: $\Sigma F_x = \textbf{-}2*\frac{4F}{5}$

 

[haruspex]

You appear to have written the vertical component as 4/3 F, twice, instead of 4/5, and the horizontal once as 4/3 instead of 3/5.

Which point are you taking moments about?