Let us consider that the man sold x screened shirts.
Accordingly, he sold 3 times as many tie-dyed t shirts as silk screened shirts and he sold 156 shirts together.
Therefore,
[tex]\begin{gathered} 3x+x=156 \\ 4x=156 \\ x=39 \end{gathered}[/tex]Therefore, the number of silk screened shirts sold is 39.
So, the number of tie dyed shirts is
[tex]39\times3=117[/tex]Hence, The number of tie-dyed shirts is 117.