R(-4,4) s(3,4) t(3,2) translate 1 unit left and 6 units down

Words such as 'left' and 'right' = x-values. When you hear these words, think about running across the x-axis. Left means running back, right means running forward. 

Up and down = y values. When you hear these words, think about jumping up or down. 

* Up and right signify positive numbers and/or increase (+)

* Down and left signify negative numbers and/or decrease (-)

In addition, note that ordered pairs are formatted like (x,y). Also note that you add ' to the original point letter when translated. 
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With that being said:

1 unit left = x - 1 
6 units down = y - 6

R(-4,4) -> (-4 - 1, 4 - 6) -> (-5, -2).

So R(-4,4) -> R'(-5,-2)

S(3,4) -> (3 - 1, 4-6) -> (2,-2)
So S(3,4) -> S'(2,-2)

T(3,2) -> (3 - 1, 2 - 6) -> (2,-4)
So T(3,2) -> T'(2,-4)