What brought me to your port was the Title of your story, the brief description of your story, and that it was a short short story (I don't normally prefer to read long ones).
I liked your choice of words and the layout of the story...there were no spelling mistakes.
I liked the twist at the ending where the wife without further question got the shovel.
The only advice I might offer is to embellish the story a little or maybe make it a little longer. I'd like to know how a housewife would dig a grave in broad daylight. Also, you might consider breaking the story up into a series of paragraphs instead of one long one. This is how I would break it up:
The suited detective arrived at my doorstep he flashed his shiny badge to show authority. It was 9:23 AM. “May I come in?” the detective asked. I moved aside and showed him to the den. “Would you like some coffee? Fresh brewed.” I offered, attempting to cover the guilt. I poured a mug for the man and watched as he suspiciously looked around the den.
“So what’s this about Officer?” I asked while handing the cup of hot coffee. “Well there has been a missing persons report for a person your husband works with.” As he talked about the man I sipped my coffee, acting interested. “Well I’m sorry to hear about this, but this is the first time I’m hearing about this, my husband leaves around 7:30 each morning, he gets back at six. Maybe you could come back around that time, you could get more information then.” He wasn’t satisfied.
“I realize that, but I’d just like to ask you a few questions, if you don’t mind.” I agreed and the investigation began. “Well this man went by the name of Greg Harmon, he was reported missing Sunday around eight o’clock…” he said before being interrupted by the phone. “I’m really sorry, excuse me Officer.”
I walked casually to the kitchen and answered the phone. “Hello?” “Honey, I have to ask you a question.” My husband said. “Well what is it?” I asked, my heart slightly dropping. “Has a detective been around the house this morning?” “Yes…” “Get rid of the body.” He said quietly then quickly hanging up.
I walked back to the den, “I’m sorry but maybe you could return later?” I showed him to the door, removed my diamond earrings and retrieved a shovel from the shed.