convert h$($t$)$ to h$($t$-\backslash$tau $)$ and x$($t$)$ to x$(\backslash$tau $)$

i need every step and in every step convolution integral and sketch step

and cases is:

case $1$ : t $<mtext\; id="EditorElement\_6683962"></mtext><mn\; id="EditorElement\_6683963">3</mn>$

case $2$: t $<mtext\; id="EditorElement\_6683981"></mtext><mn\; id="EditorElement\_6683982">4</mn>$

case $3$ : t $<mtext\; id="EditorElement\_6684002"></mtext><mn\; id="EditorElement\_6684003">6</mn>$

case $4$ : t $<mtext\; id="EditorElement\_6684024"></mtext><mn\; id="EditorElement\_6684025">7</mn>$

case $5$ : t $>=7$

and Why are there only $5$ cases?